NUCLEAR
INSTRUMENTS
AND
METHODS
158 ( 1 9 7 9 )
1-31 ;
(~)
NORTH-HOLLAND
PUBLISHING
CO.
STATUS OF TIMING WITH PLASTIC SCINTILLATION DETECTORS
M. MOSZYlqSK1
Institute Qf Nuclear Research, Swierk, 05-400 Otwock, Poland
and
B. BENGTSON
Institute of Physics, University of Aarhus, D.K. 8000 Aarhus C, Denmark
Received 8 May 1978
Timing properties of scintillators and photomultipliers as well as theoretical and experimental studies of time resolution
of scintillation counters are reviewed.
Predictions of the theory of the scintillation pulse generation process are compared with the data on the light pulse
shape from small samples, in which the light pulse shape depends only on the composition of the scintillator. For larger
samples the influence of the light collection process and the self-absorption process on the light pulse shape are
discussed. The data on rise times, fwhm's, decay times and light yield of several commercial scintillators used in timing
are collected.
The next part of the paper deals with the properties of photomultipliers. The sources of time uncertainties in photomultipliers as a spread of the initial velocity of photoelectrons, emission of photoelectrons under different angles and
from different points at the photocathode, the time spread and the gain dispersion introduced by electron multiplier are
reviewed. The experimental data on the time jitter, single electron response and photoelectron yield of some fast photomultipliers are collected.
As the time resolution of the timing systems with scintillation counters depends also on time pick-off units, a short
presentation of the timing methods is given. The discussion of timing theories is followed by a review of experimental
studies of the time resolution of scintillation counters.
The paper is ended by an analysis of prospects on further progress of the subnanosecond timing with scintillation counters.
1. Introduction
In many physics experiments a need arises to
measure short time intervals with a good resolution and accuracy. Such experiments are mean
life-time measurements of excited states, angular
correlation function, time-of-flight measurements.
Physicists studying high-energy particles need
high resolution fast coincidence systems to observe rare particles against a large background of
other events. Sophisticated counter telescopes, employing a sequence of counters in coincidence and
anticoincidence are used for particle, energy or
event selection, and for studying the decay of fast
particles in flight.
Several different nuclear radiation detectors are
used in timing experiments: scintillation counters
with organic and NaI(TI) scintillators, Cherenkov
detectors, multiwire proportional chambers, semiconductor detectors. Scintillation counters with organic scintillators, however, are still superior to
produce the best time resolution, as well as to be
used in a variety of different applications. Detection of ~,-rays and B-particles in life-time measure-
merits, neutrons in time-of-flight experiments,
dE/dx particle identification methods with thin
scintillation foils, these are some of the possible
applications.
Taking into account the great variety in size,
shape and constitution, the possibility to work
with a very high counting
rate up to
10 7 pulses/sec, it all makes them still very attractive and necessary in the many experiments in
low- and high-energy nuclear physics.
The time resolution of scintillation counters is
generally determined by the method used in the
so-called delayed-coincidence technique which is
widely applicable for the measurements of short
nuclear life-times. The technique involves the
measurements of time delay between the formation and subsequent decay of the nuclear state of
interest. Fig. la shows the simplified block diagram of the basic time spectrometer. Time pick-off
units are used to process the pulses provided by
the detectors in such a way to define the time of
occurence of the detected events, as well as to
optimise the time resolution of the system. The
"2
M. MOSZYlqSKi AND B. BENGTSON
fO4
FWHM
U~
P,
i'F:
fO5
start
fO2
stop
Oo
fOt
CHANNEL NUMBER
Fig. 1. Simplified block diagram of the time spectrometer (a) and the time distribution spectrum of the prompt coincidences (b).
The figure of merits: fwhm and logarithmic slope are marked on the spectrum,
time-to-pulse-height converter produces an output
pulse with a height proportional to the time interval between input pulses from the detectors.
The time resolution of a timing system can be
determined by measuring the distribution of the
time delays between prompt events. A so-called
prompt time spectrum is shown in fig. lb. The figure of merit of a system is usually characterised
by the full width at half maximum (fwhm) and
the approximate logarithmic slope. The time resolution contributions can be associated with three
phases of the timing process:
1) time variations in the interactions of the radiations with the detectors,
2) time variations in the response of the detectors
to the radiations,
3) time variations associated with the electronic
equipment.
Group (1) includes the variations in the source
or target to detector flight times of the radiations,
time characteristics of pulsed beam timing and
time variation resulting from the interaction of the
radiation over the detector dimensions. Although
the minimisation of these time resolution contributions is rather straightforward, it very often produces a basic limitation of the obtainable time resolution.
Group (3) refers to the intrinsic time resolution
of the electronic equipment, stability, time varia-
tion of time pick-off units and effect of electronic
noise.
The contribution of group (2) relates to the time
variations in the formation of the detector signal.
This effect manifests itself in the shape of the detector signal, namely, the finite rise time, variation
in the rise time and pulse height fluctuations, and
it depends on the statistics of information carrie r s - p h o t o n s and photoelectrons in the case of
scintillation counters.
A process of nuclear radiation detection in the
scintillation counter leads to several sources of
time uncertainties and it can be summarised as
follows:
1) The energy transfer from the detected nuclear
particles to the optical levels in the scintillator.
2) The finite decay time of light emitting states
in the scintillator and the light yield of the
scintillator as a function of the energy of the
detected radiation.
3) Variation of the time of light collection from
the scintillator at the photocathode.
4) Efficiency of conversion of photons from the
scintillator at the photocathode and the absolute number of photoelectrons.
5) Variation of transit times of photoelectrons
from the photocathode to the first dynode.
6) Variation of the multiplication process in the
electron multiplier.
T I M I N G WITH PLASTIC S C I N T I L L A T I O N D E T E C T O R S
3
Furthermore, the timing with the scintillation times and light yield of several commercial scintillators used in timing are collected. Section 3
counter depends on:
7) Single electron response representing the fre- deals with the properties of photomultipliers. The
sources of time uncertainties in photomultipliers
quency bandwidth of the photomultiplier.
as a spread of the initial velocity of photoelec8) Type of timing processing.
Processes (1) to (3) refer to the properties of the trons, emission of photoelectrons under different
scintillator and they are reflected in the shape and angles and from different points on the photocaintensity of the light pulse. Points (4) to (7) are re- thode, the time spread and the gain dispersion inlated to the properties of the photomultiplier. troduced by electron multipliers are reviewed. The
Point (8) represents the method of electrical pulse experimental data on the time jitter, single eleccollection from the photomultiplier. Fig. 2 shows tron response and photoelectron yield of some fast
the distribution of the current pulses from the photomultipliers are collected. As the time resoluscintillation counter, following ref. 1, calculated by tion of timing systems with scintillation counters
a Monte Carlo method for a mean number of pho- depends also on the time pick-off units, a short
toelectrons equal to 100. Note a large distribution presentation of the timing method is given in secof the pulse height and the rise times which re- tion 4. The discussion of timing theories in secflects the influence of the above summarised pro- tion 5 is followed by a review of experimental stucesses on the time spread of the scintillation coun- dies of the time resolution of scintillation counters. The paper is ended by an analysis of proters.
The various aspects of electronics timing with spects on further progress of timing with scintillascintillation counters have been collected in the tion counters.
past by Bell2), Schwarzschild3), Bonitz4), BellS),
Ogata et al.6), Meiling and Stary7), Schwarzschild
and Warburton 8) Williams and Gedcke 9) and Fos- 2. Scintillators
san and Warburtont°). The theory of timing has 2.1. SMALL SAMPLES t
According to the theory of the light generation
been reviewed by Gatti and Svelto~l).
process
in organic scintillators ~2'13) the detection of
In the following the present state of knowledge
of the timing properties of scintillation counters nuclear particles is equivalent to a &Dirac excitawith organic scintillators is given. In section 2 pre- tion of the lowest excited state of a crystal or a
dictions of the theory of the scintillation pulse solvent in scintillating solutions. All preceding
generation process are compared with the data on processes such as ion recombination, internal conthe light pulse shape from small samples, in which version from higher excited states of X, which
the light pulse shape depends only on the compo- yield molecules X in their lowest excited singlet
sition of the scintillator. For larger samples the in- ~X states, are considered to be much faster than
fluence of the light collection process and the self- the final emission of the light.
In a unitary scintillator (a crystal, for example)
absorption process on the light pulse shape are
discussed. The data on rise times, fwhm, decay which is transparent to its own fluorescence, the
scintillation pulse is described by a single exponential function, as follows:
I
6
i
I
i
i
i
I
i
I
~-- Ioo
i(t)
=
- -1 e - ' / ' M ,
(l)
"~M
where r M is the molecular decay time constant.
If the crystal absorbs a fraction (a) of its own fluorescence, it provides to increase the decay time
constant and in eq. (1) rM is replaced by zk~, the
technical decay time constant, which is given
Fig. 2. The distribution of the current pulse shapes from the
scintillation counter, calculated by the Monte Carlo method for
N = 100 photoelectrons (following reL 1).
t Samples of scintillators in which the light pulse shape is not
affected by the volume and only depends on the composition of the scintillator. Polished samples with thickness below 5 mm are regarded as small ones.
4
M. MOSZYlqSKI AND B. BENGTSON
[ty]
byl2,14)
=
-
TM
1-aq
'
(2)
'
(5)
and
3OO0
where a is the probability of re-absorption of flu- [ ' Ylo -- 2ha/2 N R ~
(6)
orescence photons, ~ the quantum efficiency of
the scintillator.
is the "critical molar concentration"
In the scintillating solutions .the shape of the where
light pulse depends on the energy transfer process N is Avogadro's number,
from the solvent X to the solute Y in binary sys- R o the critical energy transfer radius.
tems, and to the wavelength shifter Z, to provide
Typical scintillation pulse shapes evaluated from
a better matching to photomultiplier spectral sen- eq. (3) for binary liquid scintillators and from eq.
sitivity, in ternary solutions. Birks ~2) and Birks (4) for binary plastics have been shown in ref. 12.
and PringlC 3) have studied both theoretically and A comparison of the fastest liquid and plastic scinexperimentally the light pulse shapes from several tillators containing the same solute shows that in
organic liquid and plastic scintillators. They have the plastics a more rapid initial rise is expected. It
derived a general description of the light pulse reflects the difference between Forster and
from the binary and ternary liquid scintillators and Stern-Volmer kinetics. The rate of the Forster enthe binary plastics in terms of molecular parame- ergy transfer is initially rapid owing to the transfer
ters.
to Y molecules from close lying molecules, but it
In the binary liquid scintillators a complete decreases with an increase in time when transfer
"statistical mixing" of solvent molecules X and to more distant molecules of Y occurs.
solute Y occurs owing to molecular diffusion and
Experimentally the light pulse shape from scinX excitation migration, so that the energy transfer tillators is studied by the so-called single photon
rate is independent of time. The energy transfer method due to Bollinger and Thomas~7). In this
process obeys Stern-Voimer kineticslS), and the method the scintillator under investigation is
scintillation light pulse according to Birks ~2) is de- coupled well to the photomultiplier in the referscribed as follows:
ence counter to produce an accurate timing signal
but very weakly to the other one so that only one
i(t) = ~
(e-'/~--e -'/~i)
(3) photoelectron is produced for every - 5 0 light
"C--T 1
flashes in the scintillatorT). The time distribution
where
spectrum observed at the output of the time-tor is the fluorescence decay time constant of so- pulse-height converter combines the effect of the
lute Y,
illumination function i(t) and the instrumental rer~ is the decay time of the solvent X in the pres- sponse function fp(t) of the timing system, as folence of solute Y.
lows:
In binary plastic scintillators molecules of the
i*(t) = i(t)* f p ( t ) .
(7)
solute X and the solvent Y remain effectively stationary, apart from possible Brownian rotation dur- The function of the system response is mainly due
ing the energy transfer process, so that the trans- to the time jitter of the photomultiplier detecting
fer rate decreases with an increase in time. The single photons. The fwhm of this function varies
energy transfer process is described by Forster ki- between 0,25 ns and 1 ns, depending on the qualnetics ~6) assuming a long-range radiationless di- ity of the photomultiplier used. The time jitter of
pole-dipole interaction process. Birks m2) has de- fast photomultipliers and methods of determinarived the Forster kinetics relations for the scintil- tion are discussed in section 3.
lation pulse shape of binary plastic solutions. At
Birks and Pringle ~3) have shown that the scinhigh molar concentration [J Y] of the solute, the tillation pulse shapes found experimentally for bipulse shape is of the form~2,13):
nary liquid scintillators agree well with those calculated
using eq. (3). For plastic scintillators it is
i(t) ,,~ e -'/" - e -,/''-2~('/'')'''
(4)
stated that because of the complexity of eq. (4) the
where z~ and r are the decay time constants of generation of the synthetic pulse shapes and their
the solvent and solute, respectively,
convolution with the instrumental response func-
T I M I N G WITH PLASTIC S C I N T I L L A T I O N D E T E C T O R S
tion to fit experimental curves has been considered impractical.
As eqs. (3) and (4) differ weakly, eq. (3) is commonly used to describe the light pulses also from
plastic scintillatorstS-22). It has been proposed by
Raviart and Koechlin ~8) and verified by Lynch 2°)
and Kuchnir and Lynch 2t) for liquid and plastic
scintillators based on the light pulse shape study
by the single photon method~7).
The timing study 23-2s) with plastic scintillation
counters has shown, however, a need to assume a
slow initial rise of the light pulse to interpret the
timing properties of the counter. As a consequence, the following convolution has been proposed to describe the light pulse shape from plastic scintillators:
scintillator, were about a factor of two larger than
those expected from the shape of the light pulse
according to eq. (3).
The direct test of the validity of eq. (8) to describe the light pulse shape from fast binary plastics has been performed in refs. 28 and 29. The
light pulse shapes from the NE 111 scintillator and
the modified NE 111 scintillators by adding
quench agents 3°) have been measured by the
single photon method using C31024 photomultipliers. A fit of eq. (8), convoluted with the prompt
response of the system (fwhm = 250 ps), to the
measured time distribution of the light, pulses has
shown that eq. (8) is able to reproduce in detail
the shape of the light pulse from small
(~) = 2.5 cm, h = 5 mm) polished or black samples
of NE 111. Similar fitting tests performed with
eqs. (3) and (4) have not been successful to reflect
the initial slow rise of the measured pulse (see
fig. 3).
According to ref. 28, the initial slow rise, approximated by the Gaussian function in eq. (8),
may come from the finite times of de-excitation of
several higher levels of the solvent molecules excited by nuclear particles. This process precedes
the intermolecular energy transfer which is considered in the theory of scintillators~2'13). As the
intermolecular energy transfer process in binary
plastics (such as Ne 111) is expected 12) to be fast,
it is not reflected in eq. (8). Thus the rise time of
the light pulses seems to be controlled by preceding processes in the detection mechanism of nu-
(8)
i(t) = f o ( t ) * e -'1",
where
,/~. (t) is the clipped Gaussian function shifted by
2.5a, which represents the rate of the energy transfered from the detected nuclear
particle to the optical levels of the solute,
r
is the decay time constant of the scintillator.
The above suggestion was confirmed in refs. 26
and 27 by the measurements of the arrival time of
a fixed fraction of the total collected light of a
scintillating pulse with respect to the impinging
time of nuclear radiation represented by Cherenkov light generated in the photomultiplier window. The observed delays, characteristic for each
i0 s
,
,
,
,
~
,
,
,
,
,
i(t)-(e-tt~-e-t I rf21~ltl¢~} v z ). fp~(t)
i(t) = (e=t/t- e'-t/~l) - fpH(t)
"c=l/-.ns
f
,
,
,
i(t)=f (t) • e-tlt-fpM(t)
1:=1.3 ns
r~=11ns
lt=6
tl=O.15nS
5
OET = 0.2
ns
t =1.45 ns
I0 L
Z
O
u
U.
0
n,
UJ
(33
%"..
NE 111
=2.5crn h=0.Scrn
10 3
z
potished
1ch=62ps
10;~71]0 ' 7½0 ' 740
760
'
700
'
7'90
'
7/~0
'
760
i
=
i
720
I
I
740
i
I
760
I
/uO
CHANNEL NUMBER
Fig. 3. Fits of eqs. (3), (4) and (8) convoluted with the prompt spectrum of the system to the light pulse measured with the
polished 5 mm thick sample of NE 111 scintillator. Note that eq. (8) is only able to reflect an initial slope of the experimental
pulse shape (from ref. 28).
M. MOSZYIqSKI AND B. BENGTSON
clear radiation in plastic scintillators. The observed
slow initial rise of the light pulse, approximated
also by eq. (8), from the sample of the PVT (polyvinyltoluene)29), commonly used as a solvent in
plastic scintillators, as well as from stilbene and
anthracene samples 3~) seems to confirm the above
hypothesis. Note that for unitary scintillators the
theory of light generation process ~2) predicts a
light pulse shape of the form given by eq. (1).
The recently reported study of the light pulse
shape in refs. 32 and 33 seems to be, however, in
contrast to the above discussed eq. (8). A much
faster rise time, equal to 130 ps, of the light pulse
from the NE 111 scintillator than that found in
ref. 28 (350 ps), as well as a significantly lower
fwhm of the light pulses from quenched NE 111
plastics than those observed in ref. 29 have been
measured. In the study presented in refs. 30 and
32 the samples of the scintillators were excited by
the 50 ps wide pulses of electrons from the linear
accelerator. Sampling techniques were used to record the signal from a fast vacuum photodiode.
The fwhm of the system response, equal to
115 ps, was measured with Cherenkov radiation.
In the study reported in ref. 33 the scintillators
were excited by the 100-180 ps wide X-ray pulses
generated by the laser, and the light pulses were
recorded by a streak camera. Since the basic resolution of the streak camera was 20 ps, the measurements were limited by the fwhm of the X-ray
pulse. The results of this experiment, however,
were not consistent with those obtained in the
Linac experiment32). The fwhm of the light pulse
from the NE 111 scintillator, equal to 0.4 ns, was
far too small compared to the observed
f w h m ( = l . 2 ns) in refs. 28, 29 and 32. It shows
that a significant internal disagreement exists in
the results of all the discussed experiments from
ref. 28, 32 and 33. A detailed comparison of the
data from the above experiments and analysis of
the experimental conditions suggest 29) that a basic
difference of the energy of the scintillators excitation should be pointed out. Eq. (8) is concluded from the study of the light pulse shape by
the single photon method28'29), and the scintillators were excited by ~,-rays or electrons of about
200-500 keV on average, typical for low-energy
physics. In the Linac experiment the energy of the
scintillator excitation may be estimated to be equal
to about 108 MeV/Linac pulse32,4t). In the case
of the X-rays experiment the energy of the
scintillator excitation
is of the order of
10~°-1012 MeV/X-ray pulse. It is difficult to predict at the moment what are the properties of
scintillators at so high an energy of scintillator excitation.
The above discussed binary plastics have one
drawback in that the emitted light is strongly absorbed inside the scintillators. Therefore to work
with large samples one has to use ternary plastics.
In earlier years it assured also a better matching
of the emitted light to the spectral sensitivity of
photomultipliers. The ternary plastics differ from
the binary ones in that the energy is additionally
transferred to the wavelength shifter before the
light is emitted. For liquid scintillators, according
to Birks~2), the light pulse shape is described as
follows:
i(t) ,,~ z - v 2 e -'/'' + ~ 1 - z
• "z2
T'~I
e -'/'2 + ~ 2 - T 1 e -'/',
zz'zl
(9)
where
r~ and r2 are the decay time constants of the solvent in the presence of the primary solute, and primary solute in the presence of the wavelength shifter, respectively,
r
is the decay time constant of the wavelength-shifter.
In the case of the ternary plastics there is no
equation describing the light pulse shape derived
from the Forster kineticst2). It has been only verified by Bennet 34) that the Forster kinetics is applicable to the solute-solute transfer in organic solutions. Eq. (9) may be used also for the ternary
plastics as a good approximation22). The light pulse
shape of the ternary plastics was studied by
Lynch 2°) and the two-exponential description according to eq. (3) was used to reflect the shape of
measured pulses.
The study of the light pulse shape performed in
ref. 28 leads, however, to the other equation to describe the scintillating pulse from the ternary plastics, as follows:
i(t) = f c ( t ) * (e - ' / ~ - e - ' ; ' ' ) ,
(10)
where.IS (t) is the Gaussian function describing the
rate of the energy transfer from the detected radiations to the primary solute, and the exponential
functions describe the energy transfer process to
the wavelength shifter (rl) and final emission of
the light (r).
The validity of eq. (10) was verified in ref. 28 by
the study of the scintillation pulse from NE 104
and KL 236 scintillators (see fig. 4).
TIMING
lOSl
,
'
,
,
,
,
~
/
~
WITH
PLASTIC
SCINTILLATION
,
,
,
NE 104
O~[r=0.2 ns
DETECTORS
7
time of photons is given approximately by the relation:
T =16ns
(11)
fL(t) = ~ e--'/'L
(7L
with
c¢h
O'L=
i
o
xl
/
~
T= 1.5ns
(12)
Vo=
where
(Z
is a factor depending on the type of the reflecting surface and the optical matching at the
i
10 8
700
I
720
'
7140 '
CHANNEL NUMBER
760
'
/I"
\
780
Fig. 4. Light pulse shapes measured for the 5 mm thick polished NE I04 and KL 236 ternary plastics. Full lines represents
the best fit of eq. (]0) to the distribution of the experimental
10 6
points (from ref. 28).
x 10-2 h : 2.5cm
2.2. THICK SAMPLES
All the above considerations may be directly applied to thin samples of scintillators where the
light pulse shape depends only on the composition
of the scintillator. For larger samples the light collection p r o c e s s 35-38) influences significantly the
light pulse shape. Self-absorption and re-emission
processes are considered to increase the decay
time constant according to eq. (2). In ternary solutions, the energy transfer to the wavelength
shifter occurs both radiationlessly and radiatively]2). The efficiency of the last process depends on
the dimensions of the sample and it is reflected in
the shape of the light pulse. The influence of the
primary, unshifted light from the ternary NE 102A
scintillator has been clearly seen in the study of
the light pulse shape from thin scintillator foils.
The strong reduction of the fwhm and the decay
time constant has been observed with foils thinner
than 400/~g/cm 2 39).
0 10 ~
10 '
10 3
_ '-17 T'=°°'7
C % X p
10 2 _
~
I
700
2.2.1. Light collection process
Theoretical investigations of the light collection
process in cylindrical scintillators 35'36) have shown
that the probability density function of the transit
~
I'
2'-L'ED- - - -~'
'
J
perspex samples coated
\
I
with NE 560 paint
~= 2.5cm h = 1- 5cm
~
I
t
720
74.0
CHANNEL
I ,
760
J
780
NUMBER
Fig. 5. Time distribution spectra of the collected light measured with the samples coated with NE 560 white reflecting
paint. The insert shows the arrangement used in the experiment (from ref. 38).
"8
M. M O S Z Y l q S K I
A N D B. B E N G T S O N
scintillator exit (o~=3 for a non-specular surface),
h is the height of the scintillator,
V0 the velocity of light.
The experimental study of the time spread of
the light collection process was reported in refs. 38
and 40. Sipp and Miehe 4°) have studied cylindrical
liquid scintillators coated with aluminium foil and
concluded that time spread associated with the
light collection process is not of importance compared to the self-absorption and re-emission process. The study performed in ref. 38 for the samples of perspex coated with white reflecting paint
has shown on the contrary that the light collection
process introduces a large time spread which influences strongly the light pulse shape 2s) and the
time resolution of the scintillation counter24). Fig.
5 shows the time distribution spectra of the collected light measured with samples coated with
NE 560 reflecting paint for the point light source
placed in the centre of the top surface of the cylindrical sample. A pure exponential decay caused
by the time spread of the collected light was observed with the decay time constant increasing
with the height of the sample. Fig. 6 presents the
standard deviation a L of the transit times of light
collected from the samples coated with NE 560
reflecting paint in comparison to the Nutt 36) and
the Cocchi and Rota 35) predictions. The whole study
of ref. 38 confirms N u t r s predictions 36) that the
probability density function of the transit time of
photons is represented well by a single exponential
function. The standard deviation trL is proportional
to -the height of the samples for a fixed diameter
and depends on the quality of the reflecting surfaces. To interpret the larger values of trL found in
the experiment compared to the calculated ones,
back reflections from the boundary between the
glass window of the photomultiplier and the photocathode itself were postulated.
2.2.2. Light pulse shapes from thick samples
of scintillators
The influence of a larger volume of the scintillator on the light pulse shape has been observed
by Lyons and Stevens 4j) and studied by Sipp and
Miehe 4°) and Moszyfiski and Bengtson28). Fig. 7
shows the time distribution spectra of the light
pulses from binary liquid scintillators (BIBUQ in
xylene) of different height excited by /3-rays as
measured by Sipp and Miehe. The large widening
of the decay time constant from 1.28 ns to 1.94 ns
was observed when the height of the scintillator
was increased from 0.2 cm to 5 cm.
A quantitative study of the light pulse shape
from larger volume scintillators performed for the
NE 111, NE 104 and KL 236 plastics is reported in
ref. 28. The samples were coated with white reflecting paint and the separated scintillators tech1041
O'L
I
[n~]
I
I
I
I
I
I
I
0= 2.5cm
npM =1.52
t2
36) n
¢ Nutt
/
/
1.0
/l"
0.8
~ / n s c = 0.85
io a
sC f NE 560 np~, = 1.49
Q6
z~
10z
eta
¢
02
I ~
0
S
"Cocchi• and Rota
~"
35~npM
/nsc = 1
I
I
I
I
I
I
I
I
I
2
3
4
5
6
7
8 h[cm]
Fig. 6. Standard deviation of the transit times of photons
found experimentally for the perspex samples coated with
white reflecting paint in comparison to the calculated ones ac-
cording to Nutt 36) and Cocchi and Rota 35) predictions (from
ref. 37).
lo'Ul0
I
2
I
I
3
~
5
TIME ( n s )
i
I
6
7
Fig. 7. The time distribution spectra of the light pulses from
the binary liquid scintillator (BIBUQ in Xylene) excited by flrays; the curves A, B, C correspond respectively to height of
the sample equal to 5, I and 0.2 cm (from reE 40).
TIMING
WITH P L A S T I C
SCINTILLATION
i
i
i
i
Trctnsmission
t~
h_=Icm
9
DETECTORS
i
spectrct of the light
filters
-",2 ~hite"
,~ 0.5
z
h=0.5cm
,,while"
104
i
i
i
FWHM
0
u
3
I.L
0
h=0.Scm
,, block"
t.u
m
z
10a
2
~
NE 104
u
1
300
I
7
I
I
720
I
740
I
I
760
I
I
7BO
CHANNEL NUNBER
Fig. 8. Time distribution spectra of the light pulses measured
with the 0.5cm and l cm thick " w h i t e " samples and the
0.5cm thick " b l a c k " sample of the NE 104 scintillator
(points). Dashed lines were calculated convoluting eq. (I0) with
the measured time distribution spectra of the collected light.
full line on the pulse from the 0.5 cm " w h i t e " sample was
calculated assuming larger time spread of the collected light
than that measured experimentally. The full line on the pulse
from the 1 cm thick " w h i t e " sample was calculated assuming
a subsequent self-absorption and re-emission process according
to eq. (13). The best fit for the black sample was obtained by
lowering of the r I parameter in eq. (10) from 0.6 ns found for
the polished sample to 0.5 ns for the black one (from ref. 28).
nique was applied to the single photon method. It
permitted to determine independently the time
spread introduced by the light collection process
alone. The study shows that the light pulse shape
from larger volume scintillators is affected by both
the light collection and self-absorption and reemission processes (see fig. 8). Analytically, the
light pulse may be described as follows:
i(t)
=
i , ( t ) * e - ' / ` L * e -'/'~,
(13)
where
i s(t)
is the light pulse from the small sample,
according to eq. (10),
e -t/aL
the probability density function of the
photon transit time in the scintillator,
e -'/'' a term describing the self-absorption and
re-emission process.
The good fit was also observed using a larger trL
,,white"
FWHM
polished
~
,,white"
polished
a
i
400
,-/-
i
500
I
600
A [nm]
Fig. 9. Dependency of the effective decay time and fwhm of
the light pulses from the 0.5 cm thick polished and " w ~ i t e "
samples of the ternary KL236 plastic on the selected wavelengths of the emitted light. The transmission spectra of the
optical filters used in the experiments, corrected for the spectral sensitivity of the photocathode in the C31024 photomultiplier, are presented above (from ref. 28).
value than that measured experimentally, as follows:
i ( t ) ,,, is(t) • e -t/a['.
(14)
In this equation the term e -'/~L represents the
probability density function of the photon transit
time in the scintillator, including the self-absorption and re-emission process.
The evidence of the self-absorption and re-emission process is based in ref. 28 on the study of the
light pulse shape from the thin and thick ternary
samples of KL 236 plastic with passband light filters. In the self-absorption and re-emission process
the emitted light is shifted to longer wavelengths.
Thus in the measurements with selected wavelengths, the longer-wave components are more affected by this process and the larger slowing-down
of the light pulse was observed (see fig. 9).
2.3. DECAY TIME CONSTANTSTUDY
The papers which deal with the light pulse
shape study from organic scintillators were reviewed above. One should note also a number of
papers 42-46) studying the decay times of different
plastic and liquid scintillators commercially avail-
•10
M. M O S Z Y I q S K I
B. B E N G T S O N
AND
TABLE 1
TABLE 2
Effective decay t i m e s o f organic scintillator.
Rise time and f w h m o f light pulses, from fast plastic scintillators.
Scintillator
r (ns)
Small s a m p l e s
h~<0.5 c m
a
b
c
d
N E III
1.3 a, 1.5 b
Pilot U
Naton 136
1.38 c
1.64 ¢
K L 236
N E 102A
N E 104
N E 110
Pilot B
BIBUQ
1.59 b
2.2 c
1.74 b
2.9 c
1.28 d
Large s a m p l e s
h>~l c m
1.65 e, 1.7g, 1.66 h
-1.75 ~, 2.3J
1.5 f, 1.36 h, 1.5 h
1.85 f, 1.87 l, 1.6 m
2.3 g , 1.7 h
1.79 e
2.5 f' 2"41, 2"5g
1.8 ¢, 2.0g, 1.9 h
3.1 f, 3.3 n
1.69 h, 1.6 m, 1.9 ~
1.27 k, 1.67 °
Ref. 28, ~ = 2 . 5 c m , h = 5 m m ,
" b l a c k " sample.
Ref. 28, ~ = 2.5 c m , h =.5 r a m , polished sample.
Ref. 28, ~ = 12 m m , h = 2 m m , polished sample.
Ref. 40, ~ = 2.0 c m , h = 2 r a m , sides o f t h e s a m p l e coated
with a l u m i n i u m foil.
e Ref. 28, ~ = 2.5 c m , h = 1 c m , " w h i t e " sample.
f Ref. 28, light from t h e small s a m p l e ~ = 12 c m , h = 2 m m ,
t r a n s m i t t e d t h r o u g h white s a m p l e , ~ = 2.5 c m , h = I cm.
8 Ref. 13.
h Ref. 43, corrected for t h e contribution o f t h e long c o m p o nent.
i Ref. 46.
J Ref. 45.
k Ref. 43, corrected for t h e contribution o f t h e slow c o m p o nent.
I Ref. 42, ~ = 1/2", h = 1 / 2 " sample.
m Ref. 20, corrected for t h e contribution o f t h e long c o m p o nent.
n Ref. 44.
o Ref. 40, ~ = 2 c m ,
h = l c m , sides o f the sample coated with
a l u m i n i u m foil.
Scintillator
NElll
t r (ns) a
Ref. 32 Ref. 41 Ref. 28
0.13 b
0.35 b
Pilot U
KL 236
0.5 b
0.6 b
N a t o n 136
Pilot B
NE 104
0.7 b
0.7 b
0.7 b
Pilot F
NE 102A
0.9 b
0.9 b
atr
b ~
c ~
d ~
0.38 c
0.4 d
0.54 c
0.59 d
0.6 c
0.62 d
f w h m (ns)
Ref. 41
Ref. 28
1.23 b 1.21 c , 1 . 3 8 d
1.8 b
2.2 b
2.1 c, 2.23 d
2.3 b
2.4 b
2.4 b
2.32 c, 2.48 d
3.0 b
3.2 b
defined from 10% to 90% o f pulse height.
= 5 c m , h = 1.3 c m , black sample.
= 2.5 c m , h = 0.5 c m , black sample.
= 2.5 c m , h = 0.5 c m , polished sample.
was not considered and very often the size of the
samples studied was not specified. It was shown
in ref. 28 that the effective decay time constants
measured with the small samples are systematically less compared to published ones, which in turn
agree well in general with the measured ones for
the larger samples.
In table 2 the data on the rise times from 10 to
90% of the pulse height and on the fwhm of the
light pulses reported inrefs. 28, 32 and 41 are given. In the timing application both these parameters are more meaningful than the decay time.
Note that the binary NE 1 11 scintillator is superior. It shows the fastest rise time and the smallest
able. The decay time constant of the scintillation fwhm of the light pulse. The timing experipulses is measured by the single photon method 17) ments 23-25) performed with the NE 1 11 scintillator
and the effective decay time is determined from have also given the best time resolution of the
the linear part of the slope of the fast component prompt time spectrum measured with the 6°Co
of the measured pulse. In some cases 2°,21,43) the source.
decay time constants of the fast component of the
light pulse are corrected for the contribution of the 2 . 4 . LIGHT YIELD
long component. As the preceding discussion of
One of the important parameters of the scintilthe light pulse shape from the scintillators showed lation cou~ter which depends on both the scintila significant dependency of the decay time con- lator and the photomultiplier properties is the
stant on the size of the studied samples, the data number of photoelectrons released from the phofrom the literature given in table 1 are collected in tocathode per keV of energy lost in the scintillator
two groups; the decay times measured for samples by the nuclear radiation. In the past very often
with the thickness less than 5 mm, and larger this figure was estimated to be very low. Recent
than 1 cm. In the past, however, the influence of measurements performed by Lynch2°), Houdayer
the scintillator volume on the decay time constant et al. 47) and Bertolaccini et al. 48) showed 1-2 pho-
TIMING WITH PLASTIC S C I N T I L L A T I O N DETECTORS
11
TABLE 3
Light yield of some organic scintillators.
Scintillator
Anthracene
Stilbene
Naton 136
Pilot B
NE 102A
NE 111
NE 104
BIBUQ
Pilot U
Photomultiplier
Birks and
Pringle 13)
Lynch 2°,21)
100
80
45
60
58
50
100
64
39
42
Light yield a
Bertolaccini
et al. 48)
Bialkowski and
Moszyriski 49)
Nuclear
Enterprises44)
100
50
100
54, 58
60
65
55
68
70, 70
40
60
56UVP
67
58
RCA7585
56AVP
56DUVP
a Normalised to 100 for anthracene.
toelectrons per keV, which depends on the type of
scintillator and photomultiplier.
In table 3 the light yield of several scintillators
used in the timing experiments is listed as a relative figure compared to the light yield of the anthracene crystal. As the measured light yield depends on the spectral response of the photomultiplier, the size of the studied sample and the
method of reflecting surface preparation, a large
spread in the data from different references is observed.
2.5. TIMING APPLICATION
The above review of the timing properties of the
plastic scintillators leads to several conclusions
concerning the choice of the optimal scintillator
for given timing applications. For this purpose one
has to consider:
size of the scintillator,
- type,
- light yield.
For o~- and B-rays the thickness of the sample
may be easily limited to be below 5 m m ; thus the
light collection process and reabsorption process in
the polished samples would not be of importance28). A more serious problem is the case of
),-rays detection. The choice of the size of the
sample would be the result of a compromise between the efficiency of ),-ray detection and the
time spread introduced by the light collection process38). Table 4 presents a comparison of the
transit time jitter of some fast photomultipliers
used in timing applications, with the time spread
-
introduced by the light collection process in the
1 cm and 2.5 cm thick samples with the 2.5 cm diameter coated with white reflecting paint38). Note
that to utilise the rapidity of the C31024 photomultiplier it is necessary to reduce the height of the
scintillators below 5 mm. The time spread of
transit time of photons in the commonly used
1"× 1" sample is larger than the time jitter of typical fast photomultipliers. The limited size of the
sample has also the other meaning because it protects from the attenuation of the light inside the
scintillators themselves. It is specially of importance for binary plastics which exhibit a large selfabsorption.
TABLE 4
Comparison of the transit time jitter of some photomultipliers
used in timing experiments with the time spread introduced by
the light collection process (following ref. 38).
Photomultiplier
C 31024
RCA 8850
PM 2103
XP 1021
56 AVP
s See
b See
e See
d See
ref. 62.
ref. 40.
ref. 59.
ref. 57.
trpM
(ns)
0.13a
0.2 b
0.28¢
0.3 d
0.5 d
trL(ns)
0 = 2.5 cm
0 = 2.5 cm
h = 1 cm
h = 2.5 cm
sample
sample
0.2
0.5
12
M. MOSZYlqSKI AND B. BENGTSON
For time spectroscopy with the highest time resolution one has to choose a binary plastics such as
an NE 111 scintillator and the smallest possible
thickness. The light pulses from binary plastics are
generally faster than from ternary ones, as the additional energy transfer to the wavelength shifter
is omitted. Table 2 shows that at the moment the
binary NE i 11 scintillator is superior to any other
on the market. When the efficiehcy of the detection of y-rays, for example, is of importance, and
one has to use samples of the scintillators thicker
than 2 cm, ternary pastics would be recommended.
The light collection process introduces so large a
time spread, that the light yield and lower attenuation of the light inside the sample become of
importance. For these purposes the Pilot U - - t h e
fastest ternary plastic (see tables 1 and 2)--would
be the best one. The dependency of the time resolution on type and scintillator size will be discussed in section 6.3.
3. Photomultipliers
The time resolution capabilities of photomultipliers are associated with:
a) the time jitter in the transit time of electrons
travelling from photocathode to the anode,
b) numbers of photoelectrons released from the
photocathode which are a function of the photocathode sensitivity and efficiency of photoelectrons collection on the first dynode,
c) spread in the gain of the electron multiplier
which increases the pulse height distribution of
output pulses.
The optimal conditions of timing with the photomultiplier depend also on the frequency bandwidth of the photomultiplier, reflected in the socalled single electron responsC~). It represents the
shape of the output pulse of the photomultiplier
generated by the single photoelectron which
reached the first dynode.
3.1. TIME JITTEROF PHOTOMULTIPLIERS
The dispersion of the electron transit time in a
photomultiplier is considered 11,5°) to result from
the following sources of time uncertainties:
a) variations of the transit time of photoelectrons
between a photocathode and a first dynode due
to a different initial velocity of photoelectrons
and an emission of photoelectrons under different angles,
b) different transit times of photoelectrons emitted from different points at the photocathode,
c) electron time spread in the electron multiplier.
Transit time spread of photoelectrons is associated with their initial energy and direction of
emission. If the initial velocity is represented as a
spatial vector it can be resolved into two components, W, normal to the cathode and Wt parallel
to the cathode. To a first approximation 14:, determines the transit time of the electron and Wt determines the path it will be travel.
A difference At of the time of flight of photoelectrons emitted from a photocathode with the initial energy equal to Why and the energy close to
zero may be described approximately as followsS°):
At = 2X/(~e-Z)ffWh'E'
(15)
where
m and e are mass and charge of an electron,
E is the electric field intensity at the photocathode,
and
Wh, = h ( v - v o ) ,
(16)
where
h is Plank's constant,
v the frequency of incident radiations,
v0 the frequency of the photocathode sensitivity
threshold.
It can be seen from eq. (15) that the transit time
spread resulting from the initial velocity distribution is decreased by increasing the voltage between the photocathode and the first dynode. It
can not be, however, increased too much because
of the influence of the electric field intensity at
,"
b, Nz'\ I
," ', ',
", I
3V$~
Fig. I0. Broadening of the photoelectron beams due to tangential component of the initialvelocity of the electrons in the
56AVP photomultiplier (from ref. 50).
TIMING
WITH
PLASTIC
SCINTILLATION
DETECTORS
13
the gain of the first and successive
the photocathode on the noise level of photomul- g~ and g
dynodes, respectively,
tipliers. Eqs. (15) and (16) show also that the transit time spread is dependent on the wavelength of g~, and g~ the variance of the gain of the first
and successive dynodes, respectively.
the incident light. For longer wavelengths of the
It should be noted that variance of the transit
light which are close to the threshold of the photocathode sensitivity a lower transit time spread times of electrons in the multipliers is strongly remay be expected. This was confirmed experimen- duced when a high gain GaP(Cs) first dynode is
applied in the photomultiplier. According to ref.
tally in ref. 51.
The tangential initial velocity component W~, 53 It may even be omitted altogether considering
which is parallel to the cathode, shifts the point of the total time jitter of photomultipliers with a first
impact of photoelectrons at the first dynode by a high gain dynode.
Finally, the total variance of the photomultiplier
certain distance (see fig. 10) and has generally negligible influence on the change of the transit transit time may be written as follows:
timeS°). This shift depends also on the point on
2
2
aim a, +
+
(18)
the photocathode from which the electron is
emitted.
where
The transit time difference is purely geometrical tr~M is the total variance of the transit time of
in nature. It may be defined as the difference in
photomultipliers,
transit time between an electron trajectory starting tr} the variance of the transit time associated
from the centre of the photocathode and other trawith the different initial velocity,
jectories starting from other points on the surface tr~ the variance of transit time due to different
of the cathode, it being assumed that all electrons
paths travelled by photoelecti'ons.
have zero initial velocity. The transit time difference depends directly on the quality of the input
3.2. STUDYOF PHOTOMULTIPLIERTIMEJITTER
electro-optics of the photomultiplier.
Time jitter of fast photomultipliers is deterIn spite of the fact that very often the time jitmined
experimentally by the measurements of the
ter of a photomultiplier is considered to be assosingle
photoelectron
time distribution spectrum. It
ciated with the transit time spread of photoelecis
done
by
the
illumination
of the photocathode
trons between photocathode and first dynode, the
contribution of the next stages of electron multi- with subnanosecond light pulses of very low inplication can not be neglected. The same prob- tensity to produce only single photoelectrons. The
lems, which were discussed above for the input fwhm of the time spectrum of coincidences beoptics of photomultipliers, occur in the next stages tween the electrical pulses associated with the
of multiplication, but in an even more serious light pulse and single photoelectron pulses is a
measure of the time jitter of the photomultiplier.
formS°).
The measurements of the time jitter of a phoOn the other hand, because of the multiplication process of electrons in the multiplier, the in- tomultiplier to be accurate enough need light
fluence of the time jitter produced by the next pulses with a very short duration. Very often
Cherenkov light generated in small radiators is
stages is significantly reduced.
The variance a~ of the transit time of electrons used. The method of Kirkbride et al. 42) applied
through the multiplier may be written as fol- also by Lynch 2°) employs single photon sampling
of Cherenkov light excited by 6°Co y-rays which
lows52):
in coincidence excite a fast plastic scintillator
coupled
to a separate photomultiplier to produce a
tr2 - -gl
gx(g-l~) ( + g ' ) '
(17)
reference signal. Lami et al. s4) have proposed another method which uses the Cherenkov light
where
generated in the common radiator. The single
2
is
the
variance
of
the
transit
time
of
OrDiD z
electrons between first and second dy- photoelectron time spectrum of two photomultipliers has been measured by simultaneous single
node,
O~DD
the variance of the transit time of photoelectron sampling of Cherenkov light. In ref.
electrons between two successive dy- 29 the full Cherenkov light was used to produce
a reference signal and attenuated light to release
nodes,
M. MOSZY~ISK!
•14
single photoelectrons in the photomultiplier under
investigation.
The other group of methods utilises artificial
light pulse sources. Gas discharge light flash generators 7) and light emitting diode generators 55) are
employed.
Recently reverse biased electroluminescence diodes driven by an avalanche transistor pulse have
been used commonly as the source of accurately
timed subnanosecond light pulses. It is estimated 55) that the light pulse generated by the avalanche breakdown of a reverse biased light emitting diode fed by an electrical pulse having an
fwhm of about 0.5 ns produces a light pulse with
an fwhm below 200 ps. Unfortunately the emission spectrum of commonly used GaP light emitting diodes lies above 500 nm. Thus only a small
overlap with the sensitivity spectrum of S-11 or bialkali photocathodes is achieved. It was shown in
ref. 51 that single photoelectron time resolution
measured with the light emitting diode generator
may differ significantly from that expected for
4 0 0 n m light wavelengths at the maximum of
photomuitiplier sensitivity.
The single photoelectron time resolution of fast
photomultipliers was studied extensively in the
past36,5]-64). The transit time spread of photoelectrons and the time spread of electron multipliers
have been determined by measuring the single
photoelectron time jitter for a small spot at the
2000 Vq
-in e
2500V%
100
Z
90
:,o
'°!8.
,o
•
5
0.$
I-"
, ...=.o IX7
UH V ~ / ~ 0 . 6 p ,
,ooov,:
2ooovJ
0.7
'
0.8
'
0.9
--i
io.,
4o,
I
tO2 °
1.0"
AND B. BENGTSON
centre of a photocathodeSl'53'57,sg.62). A transit time
spread difference has been studied with small spot
scanning through the photocathode36.6°.6]). The influence of the electron multiplier alone may be
only estimated from eq. (17). It was done in ref.
24 for the XP 1021 photomultiplier. The standard
deviation a D , equal to 0.17 ns, has been found, assuming g] = g = 4 and O'o, D ODD calculated from
the width of the single photoelectron response]]).
The data on the time jitter of some fast photomultipliers used in timing experiments are collected in table 5. The time jitter is expressed as
the standard deviation found from the time spectra of the single photoelectrons. As the measured
value may be affected by the type of light pulse
used in the experiment the data are grouped depending on the type of light pulse source. The
time jitter measured with the gas discharge light
sources is corrected for a finite width of the light
pulse. The data taken from the experiments with
light emitting diodes are not corrected, as the
fwhm of the light pulses is estimated to be smaller
than 200ps. Some photomultipliers showed the
best single photoelectron time resolution for a focusing voltage different from that which gives the
highest photoelectrons collection. This was observed for the RCA 8850 photomultipliers in ref.
62 (see fig. 11). Fig. 12 shows an example of the
time spectrum measured by Lescovar and Lo 62)
with the RCA 8850 photomultiplier for a 1.6 mm
diameter spot in the centre of the photocathode illuminated by a light pulse (fwhm~<200 ps) from
the XP23 light emitting diode. Fig. 13 presents the
time spectrum of single photoelectrons measured
with the XP 22 light emitting diode generator for
the C31024 photomultiplieP]). The 6 mm diameter
central part of the photocathode was illuminated.
RCA 8850
SERIAL NUHBERK088/.5
=
S
i
i
I
I
I
I
I
I
I
U~
I,-
Z xl0 s
,-,
"0
®
°
~
,z
• o
ee
:':
2.5
-:
bi i
..
iio
""°
I
;'
k
V C- VFE
Vc- %1
Fig. !1. Single electron time spread and relative collection efficiency of the RCA 8850 photomultiplier as a function of the
voltage ratio between photocathode - focusing electrode and
photocathode - first dynode. Full photocathode illuminated
(from reC 62).
,-
UHV = 3000 V
F W H M = 330 ps
Fig. 12. Single electron time spread of the RCA 8850 photomultiplier with a 1.6 mm diameter area of photocathode illuminated (from ref. 62).
TIMING
WITH
PLASTIC
SCINTILLATION
DETECTORS
15
TABLE 5
T i m e jitter, apM (ps), o f s o m e fast photomultipliers.
Method of
measurement
56AVP
XPI021
XP1210
(~erenkov light
G a s discharge
light sources a
480 b
510 ¢
610 a
290 f
220 c
390 d
190 ¢
220 d
LED
generators
590 e
280 e
160 e
Photomultiplier
XP2020
280g
310 h
300 i
200J
RCA8575
RCA8850
C31024
380 r
380g
440 h
140 k
2001
160 m
200 n
140 °
115 k
170c
106J
64P
a Corrected for t h e width o f t h e light pulses.
b Ref. 54.
c Ref. 63.
d Ref. 57.
e Ref. 58.
f Ref. 28.
s Ref. 59, small spot at t h e centre of t h e p h o t o c a t h o d e .
h Ref. 59, full p h o t o c a t h o d e .
i Ref. 66.
J Ref. 51.
k Ref. 62, small spot.
I Ref. 62, full photocathode.
rn Ref. 61.
n Ref. 51, full efficiency o f photoelectrons collection.
o Ref. 51, reduced efficiency o f photoelectrons collection.
P Ref. 51, corrected for t h e contribution o f t h e light pulse, f w h m = 200 ps.
r Ref. 20.
The earlier discussed dependency of the transit
time jitter of photoelectrons on the wavelength of
the incident light was studied in ref. 51 for the
56CVP photomultiplier having an S-1 photocathode. A significant increase of the time resolution
above 30% was observed when the wavelength of
the incident light was changed from 790 nm to
580 nm (see fig. 14). This gave experimental evidence that the time jitter resulting from the spread
of the initial velocity of photoelectrons is proportional to the square root of the maximal initial energy of photoelectrons [see eq. (15)]. Based on this
conclusion the measured time jitter of C31024,
RCA8850 and XP2020 photomultipliers with the
use of the XP22 light emitting diode at 560 nm
light wavelength was recalculated to estimate the
time jitter at 400 nm, near the maximum of the
photocathode sensitivity (see table 6).
The influence of the transit time difference on
the total time jitter of photomultipliers can be observed by measurements of the single photoelec-
tron time resolution for the small spot at the centre of the photocathode and the full photocathode
open for the incident light. It shows that this influence is larger for the photomultipliers with a
first high gain dynode (see table 5). About a 30%
increase of the time jitter is observed for the
RCA8850 and C31024 photomultipliers when the
full photocathode is illuminated62).
The electron transit time difference, measured
for the C31024 photomultiplier by Lescover and
L o 6°) a s a function of the position at the photocathode surface for non-optimised and optimised
values of voltage ratio between the photocathode-focusing electrode and the photocathode-first dynode, is presented in fig. 15.
3.3. PULSE RESPONSEOF PHOTOMULTIPLIERS
The above discussed transit time spread of the
electrons has also another consequence: it widens
the response function of the photomultiplier to
•16
M. MOSZYIqSKI AND B. BENGTSON
10 ~'
10 s
!
,
c 31024
start: 1 phe /
stop;
XP 2L[
'
'
'
'
5 "6
CVP
(=far~, 1
B
'
'
~he
) 22 LED
103
I0 nm
z
-
~ lo'
8
zE~
~o 102f
.o8
I~ 20 nm
ILl
z
z 103
I01F
i
700
I channel 1 31ps
7~0
7~.0
I
Z)
760
CHANNEL NUMBER
Fig. 13. Time distribution spectrum of single photoelectrons of
the C31024 photomultiplier measured with the XP 22 light
emitting diode generator. The 6 mm diameter area at central
part of the photocathode was illuminated (from ref. 51).
v e r y s h o r t l i g h t p u l s e s ; t h u s it i n t r o d u c e s t h e f r e quency bandwidth
l i m i t a t i o n . T h e rise a n d t h e
w i d t h o f t h e o u t p u t p u l s e c a n b e d e t e r m i n e d by
summing
t h e v a r i a n c e s in t h e t r a n s i t t i m e p r o -
10~00
'
s~o
'
5~o
'
s:~o
'
:HANNEL NUMBER
Fig. 14. Time distribution spectra of single photoelectrons
measured with the 56CVP photomultiplier for different wavelengths of the incident light (from ref. 51).
d u c e d by t h e d i s p e r s i o n p h e n o m e n a
points of the photomultiplier.
at t h e v a r i o u s
TABLE 6
The estimation of the time jitter at 400 nm of some fast photomultipliers from the measured time resolution at 560 nm (following
ref. 51).
Photomultiplier
fwhm M a
(ns)
2 = 560 nm
fwhmpM b
fwhmhv c
(ns)
(ns)
E/k e
Wh v d
(V/m)
(eV)
l,Vh v d
(eV)
~ = 400 nm
fwhmhv
(ns)
fwhmpM
(ns)
C31024
0.25
0.15
0.15
13000
0.28
0.28
RCA8850
0.48 f
0.44
0.44
4400
0.84
0.84
0.33
XP2020
1.2
0.33 g
0.26
0.26
7400
0.5
0.5
0.51
0.47
0.24
8100
0.46
0.61
a Measured with the XP22 LED generator.
b Corrected for the contribution of the light pulse, fwhm = 200 ps.
c For the XP2020 corrected for the contribution of the time jitter introduced by the electron multiplier, fwhm = 2.36x0.17 ns
(following ref. 24).
d The threshold wavelength of the bialkali photocathode - 6 6 0 nm.
¢ See eq. (15), fwhm =kzlt.
r Focused for the highest current pulse.
g Focused for the best time resolution of the single photoelectron time spectrum.
TIMING
RCA
WITH
PLASTIC
SCINTILLATION
C 3102/.
TABLE 7
O.t.
c
Standard deviation trSER of the single photoelectron response
for some fast photomultipliers.
FIRST DYNODE
POSITION
0.2
X
o
1 I
M.
_u,
to -0.2
I¢1
x
0i.- -0.t.
-
17
DETECTORS
\,,o
I
I
I
I
Photomultiplier
56AVP
XP1021
XP1210
XP2020
C31024
O'SER (ns)
1.06 a
1.2 b
0.85 c
0.93 c
1.55 d
0.51 a
1.0 e
0.75 f
0
t.t)
m
-0.6
a
b
c
d
e
f
~ -0.8
W
,,J
m
-1.0 - SUPPLY VOLTAGE BETWEEN
ANODE AND CATHODE= 3500V
-20-16-I'2-II-,~ I) ~, 8 I'2 16 20
DISTANCE FROM CENTER OF PHOTOCATODE
(mm)
Fig. 15. Photoelectron transit time difference as a f u n c t i o n o f
the position at t h e p h o t o c a t h o d e s e n s i n g area in R C A C31024
p h o t o m u l t i p l i e r ( f r o m ref. 60).
In the timing theory tl) the speed of the photomultiplier response is characterised by the single
electron response which presents the shape of the
photomultiplier output pulse generated by the
single photoelectron reaching the first dynode.
The variance (tiER of the single ~lectron response
may be calculated assuming equal variances trOD
of transit times of electrons between two successive dynodes, as followsl~):
triER = (n-- 1) a2D,
(19)
where n is the number of stages of the photomultiplier.
Experimentally the shape and width of the
single electron response can be determined by observing the shape of the noise pulses, or output
pulses under single photon illumination at the
sampling scope. Typical fast photomultipliers have
O'SER equal to --1 ns (see table 7).
The definition of the single electron response
omits the influence of the variance of the transit
time of photoelectrons between photocathode and
first dynode on the output pulse, which is crucial
when the time jitter of the photomultiplier is considered. In standard photomultipliers with 10-14
dynodes the speed of the output pulse is weakly
affected by this variance. It is more pronounced in
the case of the 5-stage C31024 photomultiplier.
The rise time, equal to 0.8 ns, and fwhm = 1.8 ns
See
See
See
See
See
See
ref.
ref.
ref.
ref.
ref.
ref.
58.
25.
24.
64.
66.
68.
of the single photoelectron pulse are increased to
1.2 ns and 2.7 ns, respectively, for multielectron
pulses68).
The speed of the larger output pulses can be affected by the space charge effect in the last stages
of multiplication. This effect was well observed for
the C 31024 PM 68). The fwhm of the output pulse,
equal to 5 ns at 4 mA of the peak current, was increased to 8 ns at 7 m A . An influence of the
space charge effect on the transit time jitter of
photomultipliers at higher levels of photomultiplier illumination can also be expected~).
3.4.
PHOTOELECTRON YIELD
The time resolution of the scintillation counter
depends essentially on the number of photoelectrons released from the photocathode~l). It is obvious that this number depends on both the light
yield of the scintillator and properties of photomultipliers, as well as on the geometry of the scintillator or coupling with the photomultiplier. The
relative light yield of several scintillators was discussed in section 2.4.
The properties of photomultipliers which influence the number of photoelectrons include the
quantum efficiency of the photocathode and the
overall collection efficiency of photoelectrons at
the first dynode. The quantum efficiency of the
typical S-11 photocathode (Sb-Cs-O) used in fast
photomultipliers is equal to ~20% at 420 nm ligh t
wavelength. Important progress has been made recently due to the application of bialkali photocathodes (Sb-K-Cs) with a quantum efficiency
higher than 30% at 400 nm. The bialkali photo-
18
M. MOSZYlqSKI AND B. BENGTSON
TABLE 8
Photoelectron yield of some fast photomultipliers measured
with the NE 111 and Naton 136 plastic scintillators.
Photomultiplier
NE 111
N/keV
56AVP
56DUVP
XP1021
XP1023
RCA8575
a
b
c
d
e
See
See
See
See
See
ref.
ref.
ref.
ref.
ref.
0.44 a
1.34 c
0.9 d, 0.87 c
0.9 c
Naton 136
N/keV
0.73 b , 0.65 a
1.63 c
1.34 ¢, 1.04 b 1.2 a
1.18 a
1.4e
67.
48.
49.
25.
22.
cathode is characterised also by a low dark current.
The collection efficiency of recent photomultipliers
is about 90%. The pulse height and time fluctuations are also influenced by the homogeneity of
the photocathode and the collection efficiency
from different points on the photocathode. It was
studied by Lescovar and Lo 6°) for several RCA
photomultipliers. The results showed that the relative anode pulse height varies within +20% and
- 5 % for a distance ___18mm measured from the
centre of the photocathode of RCA 8850,
RCA 8852 and C 31024 photomultipliers. The largest anode pulse variation occurred at the edges of
the photocathode, due primarily to reduced collection efficiency.
The photoelectron yield of the photomultiplier
for a given scintillator may be measured directly
by the comparison of the mean value of the pulse
height distribution of the single photoelectrons
which determine the gain of the photomuitiplier
and the characteristic point at the energy spectrum
of radiation detected in the scintillator: edge of
the Compton spectrum for ~'-rays48), full energy
peaks of characteristic X-rays or conversion electrons49). As the measured number of photoelectrons characterise a given scintillation counter a
rather large spread is found in published data (see
table 8).
3.5. GAIN DISPERSIONOF PHOTOMULTIPLIERS
The pulse height distribution of the output
pulses from photomultipliers is caused to a large
extent by the statistical fluctuations of the multiplier gain. The statistical properties of the multi-
plier may be evaluated by the analysis of the
shape of the single photoelectron pulse height distributionS°). In this way one can eliminate all contributions to the distribution of the output pulse
originating from the photocathode and the input
optics.
The multiplication of electrons in the multiplier
is assumed to be a stochastic process, leading to
a certain distribution of electrons at the anode
characterised by 5°)
- a mean value of the multiplier gain,
- a relative variance.
If one assumes that the first stage of the multiplier has a gain gl and that all the other stages
have the same gain g, the overall gain and its variance may be represented by the following expression (for n>>l and g > l ) :
(20)
C, = g z g " - z
and
8~
-- ga,
g'~g
(21)
+ gl(g-1)'
where g~, and go are the variance of the gain of the
first and successive dynodes.
Fig. 16 presents the example of a single photoelectron pulse height spectrum of a photomultiplier
with the standard dynodes5°). The mean pulse
height of the single photoelectron is marked on
the spectrum. For comparison, fig. 17 shows the
pulse height spectrum of a few first photoelectrons
from a photomultiplier with a first high gain dynode6°). Note the well-defined peaks up to 5 photoelectrons. Owing to the high gain of the first dynode, typically g l - 5 0 , the variance e2A of the
single photoelectron distribution is strongly reduced.
dN
I
i
i
I
i
i
i
i
i
1 phe
160 ".:......~,.,V}../..
"
i- 120
(/I
Z
ILl
":-.
eo
,4
40
o
:%.
'
'
,b
'
,b
CHANNEL NUHBER
Fig. 16. Single photoelectron pulse height spectrum from a
photomultiplier with the standard dynodes. The mean height
of the single photoelectron is marked on the spectrum.
TIMING
11~ol
PLASTIC
SCINTILLATION
8850
RCA
I ~
WITH
. . . .
~t
o
:
--
j~Machlne "rime"
\I
Diseriminato,
Output Pul~
z x104
-"~J-
\
r
tJ
ou.
Iz
uJ
m
lie
-j
Z
19
DETECTORS
2.5
"
',,"
Vl
\
Pullelnput
~
~
V2
VT
Discriminator
_--Thrnhoid
0
i
I
I
I
I
,
i
I
i
CHANNELNUMBER
Fig. 17. Pulse height spectrum showing peaks corresponding to
one, two and up to five photoelectrons from RCA 8850 photomultiplier with the high gain dynode (from ref. 60).
4. Timing methods
The time resolution obtainable with a scintillation counter depends also on the method of derivation of the standard timing pulse from the output signal of the counter. The time derivation unit
or time pick-off unit permit to minimise the time
spread introduced by the scintillation counter. The
time resolution contribution coming from the electronics circuits of the time pick-offs and the timeto-pulse-height converter (see fig. 1), is generally
very small and will be omitted in the later discussion.
The most popular timing methods are the following:
a) leading-edge timing,
b) crossover timing,
c) constant fraction timing.
Leading-edge timing with a fixed threshold discriminator on the anode current pulse from the
photomultiplier is the simplest time pick-off
method. The leading-edge discriminator triggers at
a fraction h = VT/Va for a signal pulse height Va.
This fraction varies over the accepted range of
signal to pulse height Va . Owing to its simplicity, leading-edge timing has a wide application in measurements with the narrow dynamic range of input
pulse height. For a larger dynamic range the time
walk effect may dominate the time resolution of
the system.
To define the time walk consider a fast discriminator with a threshold Vr operating on detector
signals of finite rise time. Although the two
signals in fig. 18 were caused by events occurring
at the same time to, the larger signal V~ crosses
the discriminator threshold before the smaller one
p.i.
I
I
I
I
Hlight
to
tt
t2
Time
Fig. 18. Demonstrationof walk causedby the amplitude effect
and chargesensitivity of the leading-edgediscriminator (from
ref. 9).
V2. This shift in the crossing time causes the output pulse of the discriminator to walk along the
time axis as a function of pulse height. The walk
is most noticeable for pulse heights close to the discriminator threshold.
The second walk effect is due to the charge sensitivity 69,7°) of practical discriminators. Even
though the discriminator threshold has been
exceeded, a finite amount of charge q is required
to trigger the discriminator. The additional walk
time /Itq needed to collect this charge increases as
the signal decreases, and becomes very large for
signals with amplitudes Va~ VT.
The fast crossover method (clipping stub technique) was developed to overcome the serious walk
effect inherent with wide dynamic range use of
leading-edge timingT~'72). In this method the
anode current pulse is clipped with a short delay
line to produce a bipolar pulse with a zero-crossing
time. A fast crossover discriminator is used as
time pick-off device. Since the zero-crossing time
represents the same phase point for all pulse
heights, the walk effect is almost entirely cancelled. This system reduces walk very effectively and
it provides better time resolution than leadingedge timing for large dynamic ranges. For a narrow dynamic range the time resolution is worse
than with leading-edge timing 73) because the discriminator fraction of crossover timing is usually
5096, which gives a large statistical time jitter of
the scintillation counter.
A need to work with the optimal fraction in leading-edge timing and the excellent reduction of
walk provided by fast crossover timing have stimulated design of a circuit which would trigger at
•20
M. MOSZYIqSKI AND B. BENGTSON
Input
Signal
b]
Attenuat.
Signal
I-
,!t
Invertedc] F
Delayed |
I
Signal. L
Shapedd) F
Signal
m
Volt.
~--~Tim•
I/
~,
l
Fig. 19. Pulse shape and time considerations for the constant
fraction timing technique.
the optimum triggering fraction, independent of
pulse height74"T5). In the constant fraction of pulse
height trigger an attenuation-subtraction shaping
technique is used 74'75) to produce a pulse with
zero-crossing phase point (see fig. 19), which triggers the fast crossover discriminator. This phase
point has been found to be optimal at a slightly
higher fraction than that at which leading-edge,
timing gives best time resolution24). Constant fraction timing provides the best time resolution with
scintillation counters, independently of the dynamic range of pulse heights. For a narrow dynamic
range it gives 20-30% better time resolution than
that measured with leading-edge timing24).
The authors have tested several commercial
constant fraction timing units. The results are not
comparable with those obtained in ref. 24. This
agrees with information obtained from other laboratories. However, excellent results were obtained
very recently by an ORTEC model 463 timing
unit which was modified to work with integral
stretched compensation, following the idea in
ref. 24.
5. Timing theories
The timing properties of the scintillators and
photomultipliers discussed above, as well as the
influence of the timing methods used to process
the output signal, are considered and approximated in mathematical form by the timing theories 1'4'11'19'21'22'24'37'73'76-86) to explain and predict
the time resolution of the scintillation counter.
In 1950 Post and Schiff 76) first discussed the
limitations on resolving time that arise from the
statistics of photon detection. They assumed that
following the excitation of the scintillator by an
energetic event the photomultiplier amplifies the
primary photoelectrons without time spread and
that the resulting output pulse is fed into a discriminator that detects when a definite number of
photoelectrons, say n, have accumulated. From
Poisson statistics, they showed that the probability
that the nth photoelectron occurs between t and
t + d t is as follows:
P,(t) dt = e -Nr(O [NF(t)I"-I NF'(t) dt
(n - 1)!
'
(22)
where
NF(t) is the average number of photoelectrons
detected in the interval between 0 and t, following
the exciting event at t--0, F ' ( O = d F / d t ,
NF(oc)=N, the average number of photoelectrons
detected per event.
Although they assumed that there was no transit time spread in the.photomultiplier, to include
this factor requires only that F'(t) be redefined so
that the photomultiplier transit time spread P(t) is
folded in with the photocathode illumination function l(t), i.e.,
F'(t) = P(t) * I(t),
(23)
where l(t) is the probability density function of
arrival times of photons at the photocathode produced by an event at t--0, P(t) is the probability
density function of the transit time spread of electrons in the photomultiplier. The modified Post
and Schiff theory was succesfully applied by
Lynch to .predict the shape of the time spectra in
a pulse shape discrimination circuit 21) and it is
used to predict the time resolution of a scintillation counter22).
Gatti and Svelto 11'77'78) and Hyman et al. l'lg)
analysed independently the timing properties of
scintillation counters and they obtained very similar analytical formulations. The model describing
TIMING
WITH
PLASTIC
SCINTILLATION
the stystem under study can be characterised in
the following way:
The timing properties of the scintillator are
reflected by the probability density function of the
photoelectrons generated at the photocathode, l(t).
N is the mean number of photoelectrons per radiation impact on the detector. Hyman '9) has assumed an l(t) of the following form:
l (t) ,,, e - ' / ' - e -ty/',
(24)
where
r is the decay time constant of the scintillation
pulse, y = r / r ~ ,
r~ is the rise time constant of the scintillation
pulse.
The properties of the photomultiplier, according
to Gatti and Svelto 11) are contained in the single
electron response function SER. This function is
characterised by the number A of electrons at the
photomultiplier output, time h, defined as the
time between the emission of the photoelectron
from the photocathode and the centroid of the
output pulse, and by the mean square width ~. of
the SER pulse. The mean value of A is expressed
as follows:
,4 = g " - 1,
(25)
where
g is the mean gain per stage of amplification,
n the number of dynodes.
The mean value of h is the sum of the mean
transit times between successive dynodes:
h = ho + h l + . . . + h . _
1,
(26)
where
h0 is the transit time of photoelectrons between
photocathode and first dynode,
h~-h,,_t are the transit times between successive
dynodes.
The mean value of 22 is given by:
22 = ~r2 + or22+ ... + a ,2_ l ,
(27)
where trl-cr,_
2 2 ~ are the variances of transit times
between successive dynodes. If or;2 are equal and
denoted by trOD, then:
22 = ( n - 1) Cr2D.
(28)
According to Hyman ~,~9) the single electron response can be described analytically by a clipped
Gaussian function as follows:
f.(t) - (2~)~/2 2
222
(29)
DETECTORS
21
for 0~<t~<4.332, and f ~ ( t ) = 0 , for t < 0 and
t>4.433. The single electron response is considered in the theories ~1'~9) as rigid in shape but variable in height and time.
Applying Poisson statistics to the photomultiplier gain fluctuation 79) one can find the variance
e2A is given by
- g'g
g-l'
(30)
where go is the variance of the gain of the single
stage.
A more elaborate equation for e~ when the gain
of the first dynode is larger than the other ones is
presented in section 3.5 [see eq. (21)]. Hyman 1'~9)
used the quantity r to described the gain dispersion as follows:
r = (1 "1-8A2)1/2.
(31)
The statistical fluctuation of the transit time jitter of the photomultipliers was discussed in detail
in sections 3.1 and 3.2. To describe analytically
the probability density function of the time jitter
of the photomultiplier Hyman used the clipped
Gaussian function of the same form as for the single electron response [see eq. (29)], but with the
standard deviation tr.
All the statistical properties of the photomultiplier are included in the so-called "equivalent illumination function" l*(t) of the first dynode as follows:
I*(t) = I ( t ) , f o ( t ) ,
(32)
where
l(t) is the probability density function of the
photocathode illumination,
.f,(t) the probability density function of the transit
time jitter of electrons in the photomultiplier.
The output current pulse from the photomultiplier is represented by the convolution integral as
follows:
i(0 = I*(0*fa(t),
(33)
where
l*(t) is the equivalent illumination function [see
eq. (32)1,
.~(t) single electron response function.
Finally, the theory of timing considers the type of
pulse processing to define the so-called machine
time at which the standard timing pulse is generated by an electronics unit. The most important
methods of pulse processing are as follows:
22
M. MOSZYlqSKI AND B. BENGTSON
a) Straight response--the time signal is generated
when the photomultiplier current
pulse
exceeds a preselected threshold h, which is
measured as a fraction of the maximum height
of the mean pulse of the current.
b) Integral response--the time signal is generated
at the crossing of the integrated current pulse
through a preselected threshold h, which is
measured as a fraction of the total charge of
the mean pulse collected at the anode.
c) Centroid response---the time signal is referred
to the centroid of a preselected amount of
charge, collected at the anode. The fraction h
is measured with reference to the total charge
of the mean pulse collected at the anode.
Hyman ~9) has presented predictions of his
theory as a series of plots representing the time
resolution of the scintillation counter as a function
of the triggering fraction h of the output pulses.
The plots were calculated for different response
types as well as for different sets of parameters
characterizing the scintillation counter.
The standard deviation (fit) of the time measurement was normalised in the following way:
z'r
=H
h,
,;,7
•
(34)
Fig. 20 shows a family of curves according to eq.
(34) for the integral response.
The Hyman theory ~9) in its original form was
t~
'
,
.
i
•
,
i
,
a,y
a6
y=2.5
Air= 213
a~
inleqrol response
a~
o
'
'
2'o
'
Jo'
io
'h
Fig. 20. Theoretical family of the time resolution versus pulse
height fraction curves for the integral response, according to
Hyman, (ref. 19).
not successful to explain the time resolution of
the scintillation counter~l). The comparison with
experiment was not completely reliable as the
theory does not account for all the physical and
geometrical characteristics of a scintillator87). This
theory was modified in ref. 24 by the introduction
of a new description of the photocathode illumination function, as follows:
I ( 0 = fG(t) * e -'/',
(35)
where fo(t) is the clipped Gaussian function describing the generation and collection of the light in
the scintillator. As a consequence, the a parameter
in the theory representing the time jitter of the
photomultiplier was redefined in the following
way:
a 2 = a2M+ a~2=,
(36)
where a2M and a~c are the variance of the
time jitter in the photomultiplier and the scintillator, respectively.
A discussion of experiments 24) testing the modified Hyman theory is given in section 6.
Apart from the work of Gatti and S v e l t o 1t'77"78)
and Hyman et al. ~) and Hymanlg), other calculations of the time resolution of the scintillation
counter have been published based on others
methods and assumptions. Euling s°) and Donati et
al. s~) viewed the statistical events in photomultipliers as time-dependent branching process. EIWahab and Kane 82) calculated the differential probability of the arrival of the Cth photoelectron
under the assumption of exponential decaying
light emission of the scintillator and of an exponential function of the transit time spread in the
photomultiplier. More sophisticated calculations
were obtained by adding two further exponential
functions for the finite rise time of a scintillator
light pulse and for the transit time spreadS3-ss).
They can be well fitted to experimental values for
the dependency on triggering fraction without
having to consider the various machine times. Sigfridsson s6) used a similar statistical method.
The inductive method based on a Monte Carlo
calculation was proposed by Cocchi and Rota37). It
suggests a significant deviation from the theory of
Gatti and Svelto and of Hyman when the number
of photoelectrons released from the photocathode
is reduced below 100. The influence of the pulse
height selection on a real timing system was predicted by the calculations.
TIMINGWITHPLASTICSCINTILLATIONDETECTORS
6. T i m e r e s o l u t i o n s t u d y
The time resolution of scintillation counters has
been studied experimentally for about thirty years.
The progress in the best time resolution obtainable
with scintillation counters is given in table 9. It
was achieved by development of better scintillators and photomultipliers, by progress in the design of fast electronic circuits as well as by better
understanding of the timing properties of scintillation counters.
During several years three problems were studied experimentally:
- the best time resolution obtainable with scintillation counters and its relation to predictions of
the timing theories,
- d e p e n d e n c y of the time resolution on the
energy lost in the scintillator by nuclear radiation,
- the optimum of the pulse height fraction used
to trigger electronics, or more generally the
shape of the time resolution dependency on the
pulse height fraction.
The problem of interpretation of the time resolution of the scintillation counter was not easy to
solve in the past as the timing parameters of the
counter were difficult to measure by straightforward methods. The large value of the optimal
pulse height fraction observed experimentally was
hard to understand in the light of the timing theories. Several experiments 3.9°) concerning the time
resolution versus the energy lost in the scintillator
deviated from that predicted by the theorytl).
23
The recent study of the time resolution of scintillation counters presented in refs. 24 and 25
seems to explain several misunderstandings. The
better knowledge of the light pulse shape from
plastic scintillators has permitted to modify the
Hyman theory and to get reasonable agreement
between theory and experiment.
6.1. TIME RESOLUTION VERSUS ENERGY
The dependency of the time resolution versus
energy is essentially contained in N - - the average
number of photoelectrons emitted from the photocathode. Due to the statistical nature of the emission process the number of photoelectrons is distributed around the average N with a spread
which is reflected in the pulse height resolution
6E, which to a good approximation is proportional
to x/E.
When one investigates the dependency of time
resolution on absorbed energy one must be careful
to select the same fraction of the distribution of
photoelectrons for all energies. This means that
the energy window settings AE must be proportional to 6E which in turn is approximately proportional to x/E.
The time resolution versus energy was studied
in refs. 24 and 25 according to the above considerations using NE 111 scintillators and XP 1021
photomultipliers. Results of the experiment are
shown in fig. 21. For the correct choice of the
window settings the time resolution is proportional
to 1/x/E and gives an excellent agreement with the
AE/,~" = const., I.e.
[psi
600
Scintillators:
NE 111, d= 2.5crn, h= 2cm
AE/ ,~-E'E= const.+ c
X~
e
AE/E= const., I.
.cE
500
,-
.~ &00
5
o
E/E=
300
const.j
E
~= 200
100
'+"'-
l
i
I
I
I
I
I
I
l
I
0.01 0.02 0.03 0.0/, 0.05 0.06 0.07 0.08 0.09 0.1
E -t/2[keV A/2 ]
Fig. 2]. Time resolution versus energy for two types of pulse height selection for leading-edge and constant fraction timing (from
ref. 24).
"24
M. MOSZYlqSKI AND B. BENGTSON
theoretical predictions given by Gatti and
Svelto 11,77,78) and Hymanl'~9). For comparison, the
results for a window 4E proportional to E are also
shown which have been used by many
authors3'9°). Note also that the time resolution
versus energy is independent of the energy window when constant fraction timing is used in the
experiment.
6.2. TIME RESOLUTION VERSUS PULSE HEIGHT FRACTION
USED TO TRIGGER THE ELECTRONICS
The determination of the dependency of time
resolution on pulse height fraction used to trigger
has an essential meaning for the optimisation of
the time resolution of scintillation counters. The
measurements consist of a determination of the
full width at half maximum (fwhm) of the time
spectrum; the threshold of the fast discrimination
is generally constant and variation of the pulse
height fraction is affected by a calibrated attenuator3).
The value of the optimal pulse height fraction
and more generally the shape of the time resolution dependency on the pulse height fraction
determined for leading-edge timing may be directly compared with those predicted by timing theories. Thus it gives a sensitive test of the validity
of theory. A number of experiments 3'24,25'4°'87-~°1) for
various scintillators and photomultipliers have
been performed to check the theoretical predictions regarding the time resolution.
-•
t
51
/
In ref. 24 NE 111 and Naton 136 scintillators of
different dimensions coupled to XP 1021 photomultipliers were studied. The experiments showed
that the shape of the dependency of the time resolution on the pulse height fraction, and in particular the optimum value of the pulse height fraction, depend strongly on the type and dimensions
of the scintillator. The comparison of the experimental and theoretical curves according to Hyman
theory is given in fig. 22. The shape of the experimental curves measured for the different scintillators follows the shape of the theoretical curves
calculated for different parameters of photomultipliers. All the curves are normalised according to
eq. (34). As a conclusion of the above study the
modification of the Hyman theory was proposed
(see section 5), which was able to give agreement
with the results of the experiments.
In ref. 25 the additional aspects of the comparison of the experimental and theoretical time
resolution versus the pulse height fraction curves
are considered. As was discussed in section 6.2.
the experimentally observed time resolution is
dependent on the statistical distribution of the
average number N of photoelectrons at the output
of the photomultiplier, therefore, the theoretical
calculations are performed for the quantity
n = (6T> D_ I
rather than for (6t) itself,
-z
Experiment
Hyman theory
(37)
^
~
Hymon theory
o IX: 1
NAI'ON 136:
1.21- O:2.5cm h : 2 c m /
~ :2.5cm
y
1.~
"~"
1.(2
~/X=05
0.8
°o.:
O.t~
0.~
111
0.6
/~ : z/3
0./.
0.2
~
¢"
'" d : 2.5cm h : 2 c m
0:2.5cm h:lcm
•
' ¢ :1.25cm h= 0.2cm
0.2
INTEGRALRESPONSE
0'.1 0'.2 013
0'SB
0.6
0.&
0.2
0'I 0'2 0'3
0'.S
INTEGRALRESPONSE
& 0'.2 0'.3
0'.Sh
Fig. 22. Comparison of the time resolution dependency on pulse height fraction measured with the Naton 136 and NE 111 scintillators of different dimensions coupled to the XP 1021 photomultiplier with the theoretical curves of Hyman (fig. 3a and b
of ref. 19, following ref. 24).
TIMING WITH PLASTIC S C I N T I L L A T I O N
where
D
is the standard deviation of the pulse height
distribution,
(fit) the standard deviation of the time distribution
In the Hyman theory ~,19) the D factor is defined
DETECTORS
i
i
25
i
I
1.~
1A
1.~
as
(38)
1.0
where r is a quantity describing the gain dispersion [see eq. (31)].
In experimental conditions the coefficient D can
be determined from the energy resolution 6 E / E
(fwhm) of the scintillation counter measured for
the nuclear radiation, as follows:
^~ 0.8
D = r/x/N,
62
D = 1/2.36 -~-.
(39)
Recent data 2°,47,48) on the photoelectron yield
given by plastic scintillators coupled to photomultipliers lead to the conclusion that the dispersion
D is not only determined by the average number
N of photoelectrons, as in eq. (38), but also
depends on other factors. So the values of D
determined by eqs. (38) and (39) may differ substantially, even by factor of 1.5. In the conclusion
of the study of ref. 25 it was shown that a normalisation to the energy resolution of the scintillation counter seems to be more reasonable, as it
takes into account all properties of the scintillation
cou nter.
The above problem is strongly related to the
choice of the energy window width in the side
channel when one makes a comparison of the
experiments with the theory predictions. The
theory considers the average number N of photoelectrons emitted from the photocathode which
produces the Gaussian pulse height distribution at
the output of the photomultiplier. Therefore, for
the continuous energy distributions (Compton
spectra, B-rays spectra), it can be approximated by
a window width for the gating channel equal to
the energy resolution of a monoenergetic peak of
energy equal to the average one accepted in the
window.
A study 25) of the time resolution as a function
of the pulse height fraction performed following
the above conditions for a 2 m m thick NE 111
scintillator coupled to a XP 1021 photomultiplier
showed a quantitative agreement with the predictions of the modified Hyman theory. Fig. 23 presents a fit of calculated and measured curves of
0.6
0.2
0'.I ~'2
Fig. 23. The best
resolution on the
the experimental
different energies
d3
0.~
oI~ h
fit of the calculated dependency of the time
pulse height fraction [o the distribution of
points averaged over the measurements at
between 50 and 200 keY (from ref. 25).
the time resolution versus the pulse height fraction. The experimental points were averaged for
energies between 50 and 200 keV.
6.3. THE BEST TIME RESOLUTION
The experimental tests of the timing theories
were generally performed for leading-edge timing,
although the best time resolution was obtained
with constant fraction timing. Fig. 24 presents a
comparison of the time resolution versus pulse
height fraction for leading-edge and constant fraction timing24). It shows the important improvement of the time resolution even for the narrow
dynamic range and the shift of the optimal pulse
height fraction for the constant fraction timing.
The geometrical difference of the curves shows
the " w a l k " component which is cancelled by the
constant fraction timing.
The best time resolution for the scintillation
counters to date is from refs. 24, 49 and 106 (see
table 9). The fwhm = 132 ps and slope t~/2 = 18 ps
is shown on the prompt time spectrum in fig. 25,
measured with 1 cm thick and 2.5 cm diameter
NE 111 scintillators coupled to XP 1021 photomultipliers for 15% energy windows at 930 keV (6°Co
source) 24). Fig. 26 shows the effectiveness of the
constant fraction timing for a very wide dynamic
"26
[psi'
M. MOSZYI';/SKI AND B. BENGTSON
Naton 136
16= 25cm, h= 2cm
22No E=290keV /
&E/E ,~ 10%
f///
/ "
/
I.e.
[psi
/
NEll1
~= 2.5cm, h =. 0.2cm
6°Co En= 200key
6E/E,~10%
I.e.
300
.f.
3O0
E
200
--
c
9
/
"Walk"
r,
200
c.~f
component
.~ lOO
"Walk"
100
component
0'2 o'.3
0'5
0.1
0.2 03
04
05 h
Fig. 24. Comparison of the time resolution versus pulse height fraction curves for leading-edge and constant fraction timing.
The geometrical difference of the curves shows the "walk" component.
TABLE 9
Progress in the best time resolution of the scintillation counters measured with the 6°Co source.
Year
Time resolution a
fwhm
Scintillators
photomultipliers
Ref.
Stilbene
1P21
Naton 136
56AVP
Naton 136
56AVP
Naton 136
XPI020
Naton 136
RCA7850
Naton 136
XPI020
Naton 136
C70045A
NE III
XPI021
NE 111
XPI021
NE 111
XPI02I
103
103 '
(ps)
1952
2000
1963
320
1964
240
1964
210
1965
225
1966
160-200
1966
185
1970
132
1971
130
1972
130
a For two counters.
3
104
8
"6
132ps~
,
60Co
930 - 930keY
, AE/E , ~ 15'/:,
Scintillators :
NEll1 ¢= 2.5cm,
h= lcm
102
90
105
87
Z
10~
94
24
106
49
lo' 180 190 200 210 220 230
Channel number
Fig. 25. Prompt time spectrum from 6°Co source obtained
with the NE 111 scintillators on XP 1021 photomultipliers
(from ref. 24).
27
T I M I N G WITH PLASTIC S C I N T I L L A T I O N D E T E C T O R S
10'
103
I
e
I
i0~0
9 0 ~ of Compton
spectra
Scintillators:
NE 111
p-2,Scm h-lcm
[
TABLE 10
Time resolution measured 24) with the Naton 136 and NE 111
scintillators coupled to XPl021 photomultipliers.
Scintillator
1 channel -19 ps
Naton 136
ou 1~
37ps
U.
0
m
Ig
Z
NE 111
Dimensions
diam.
height
(cm)
(cm)
2.5
2.5
2.5
1.25
2.5
2.5
2.5
1.25
2.0
1.0
0.2
0.2
2.0
1,0
0.2
0.2
fwhm E l/2a
(ps MeV 1/2)
108
93
88
77
102
82
70
58
a Time resolution of one counter measured with constant
fraction timing.
101
CHANNEL NUMBER
Fig. 26. Prompt time spectrum from 6°Co source, 90% of
Compton spectra were accepted in the side channels of both
counters (from ref. 49).
range of the energy; the fwhm = 195 ps was measured with 909/0 of the 6°Co Compton spectrum
with the NE 111 scintillators and the XP 1021
photomuitiplier (from ref. 49).
The obtainable time resolution of a scintillation
counter depends also on the size of the scintillator.
The light collection process introduces a time
spread which could be larger than the time jitter
of fast photomultipliers (see sections 2.2.1. and
2.5). The self-absorption and re-emission process
affect the decay time of scintillating pulses and
according to ref. 40 cause deterioration of the time
resolution. The influence of all these processes on
the light pulse shape is reviewed in section 2.2.
Table 10 presents the time resolution normalised
to the energy measured with NE 111 and Naton
136 scintillators of different thickness24). Note that
the time resolution growth is up by a factor 1.5
when the height of the scintillator is increased
from 2 mm to 2 cm.
7. Further prospects on better timing characteristics
of scintillation counters
The discussed above properties of scintillation
counters showed that at present a time resolution
slightly larger than 100 ps for high-energy ),-rays
(6°Co source) was achieved 24'49'1°6) using XP1021
photomultipliers and 2.5 cm diameter and 1 cm
high NE 111 scintillators. For lower energies one
can note the 330 ps time resolution for 50 keV
electrons measured in coincidence with highenergy )'-rays25). All the studies showed that both
scintillators and photomultipliers are the source of
time uncertainties. Besides, the time resolution
can be strongly limited by the size of the scintillator because of the light collection process and
the time spread of the nuclear radiation interaction
in the volume of the scintillator. To improve the
time resolution of scintillation counters one has to
expect further development of faster scintillators
and photomultipliers.
7.1. SCINTILLATORS
According to the theory of the light pulse generation process in organic scintillators 12'~3) the
speed of the light pulse depends on the composition of the scintillators as follows:
- for a given solvent and solute of the binary system the speed of the light pulse improves with
the increase in the solute concentration owing
to a faster energy transfer,
- the solute should have a high solubility, a short
fluorescence lifetime and a high fluorescence
quantum yield to increase light yield,
-the
solvent should have a high yield of the
excitation of the lowest singlet state IX,
- binary scintillators are generally faster than ternary ones.
"28
M. MOSZYIqSKI AND B. BENGTSON
Based on the above criterion the NE 111 plastic
scintillator was developed and is the fastest one
on the market. It contains 40 g/! of PBD dissolved
in polyvinyltoluene (PVT). A further increase of
the solute concentration in the NE 111 solution
was not possible because of the solubility limit of
the PBD in PVT. Lyons and Hocker t°8) have proposed to exchange PBD in NE 1!1 scintillator for
butyl-PBD which has a larger solubility in PVT.
The study 33) of the speed of the light pulse from
50g/l, 100g/l and 150g/l of butyl-PBD in PVT
samples seems to suggest an improvement of the
speed of the scintillator response. A similar study
performed in ref. 29 by the single photon method
showed no difference between the light pulses
from the above samples and NE 111 plastic.
The method used by Lyons and Hocker ~°8)
reflects new possibilities for better organic scintillators. Many molecules with a high fluorescence
efficiency and short decay times but which were
relatively insoluble have been made soluble by a
substitution of alkyl or oxa-alkyl groups for hydrogen atoms at suitable locations in the molecule~°9).
Among the solutes to which this solubilization
technique has been applied, the p-oligophenylene
series is particularly promisingS°9). It has been
shown that the decay time varies inversely with
the number of phenyl rings in the molecule and
that the light yield has been larger for the longer
molecules. The BIBUQ solution in toluene or
xylene is an example of this family of scintillators2°).
The studies reported in refs. 24 and 25 seem to
suggest another limitation of the scintillation pulse
speed which is associated with the solvent itself.
The relatively slow initial rise of the light pulses
from unitary and binary scintillators was considered to result from de-excitation of several higher
levels of the solvent before the excitation of the
lowest singlet state ~X. It suggests to analyse the
solvent properties in the light of this hypothesis.
As the conversion efficiency of even the best
organic scintillators is only about 3% one would
expect improvements by further investigation of
solvents and fluors.
7.2. PHOTOMULTIPLIERS
The last years have brought important progress
in better constructions of fast photomultipliers.
The bialkali photocathode with N50% larger
quantum efficiency was introduced. High gain
dynodes (mainly the first one) reduce strongly the
contribution of the electron multiplier to the total
time jitter of the photomultiplier. The best time
resolution published up till now is still obtained,
however, with the standard XP1021 photomutipliers24,49,106). Sipp and Miehe 4°) used the
RCA 8850 photomultiplier with a high gain first
dynode but the time resolution study was performed mainly with the common scintillator coupled
to both photomultipliers. Thus the time resolution, equal to 176ps measured with B-rays of
energy about 290keV (equivalent to Compton
edge of 511 keV annihilation ),-rays from a 22Na
source), can not be compared directly to the
results obtained in the coincidence experiments. In
such an experiment with ),-rays from a 22Na
source they got fwhm = 220 ps, thus comparable
to that of the XP 1021 photomultiplier24). Very
preliminary experiments 11°) performed with the
C31024 photomultiplier seem to suggest that a
better time resolution can be obtained for energies
lower than 100 keV. For higher energies the space
charge effect may limit the speed of the photomultiplier.
A further progress of fast photomultipliers will
probably be associated with the application of
microchannel plates as the electron multiplier.
Although, photomultipliers with channel plates
are still in the development stage the microplates
themselves are already used in several timing
experiments to detect heavy ions or electrons ~L~2) showing excellent timing capabilities.
Girard and Bolore ~2) studied an arrangement
which consisted of two microchannel plate multipliers detecting electrons from a carbon foil. Fission fragments of ~z-particles from a 252Cf source
impinge on the foil at an incidence of 45 ° . The
time resolution of the arrangement was 87.5 ps for
fission fragments and 117 ps for a~-particles. Owing
to the basic symmetry of the experimental device
one can estimate the time resolution of one counter to be equal to 62 ps and 85 ps for fission fragments and a~-particles, respectively.
Development photomultipliers with channel plates were studied by several authors57'!13-116).
Recently Lo et al. ~5) have performed a general
study of performance characteristics of two development photomultipliers with the microchannel
plates LEP HR350 and HR 400. These photomultipliers have curved high gain microchannel plates
to avoid ion feedback. Proximity focusing is used
for the input and collecting stages. The HR 350
T I M I N G WITH PLASTIC S C I N T I L L A T I O N DETECTORS
photomultiplier has an S-20 photocathode with a
useful diameter of 13 mm and it incorporates a
coaxial anode. The HR 400 has a 15 mm diameter
S-20 photocathode and a simple plate as anode.
The gain of each tube was 106 . The measured
timing characteristics showed better figures for the
HR350 photomultiplier. The SER fwhm equal
to 1.25ns and 1.4ns, and rise time equal to
0.64ns and 0.9 ns, were determined for HR350
and HR400 photomultipliers, respectively. The
measured
single
photoelectron
time
spread
fwhm~<200ps was limited by the width of the
light pulse from the light emitting diode.
Taking into account a high quantum efficiency
equal to -20°A and anode pulse peak current
linear up to 260 mA, all together show that the
microchannel plates photomultipliers exhibit very
good timing capabilities, superior to the conventional ones with discrete dynodes.
7.3. OTHER LIMITATIONSOF THE TIME RESOLUTION
Faster scintillators and photomultipliers which
might be expected in the future will improve the
time resolution, but still it will be limited by the
light collection process and the spread in time of
flight of nuclear radiation. It was discussed in section 2.2.1 and reported in refs. 24 and 38. Therefore the problem to choose a scintillator size, a
small one for high time resolution or a big one for
larger detection efficiency, will be even more
severe than today.
The low efficiency of organic scintillators for Yrays makes a need to find other ones based on
materials with a high Z. For X-rays and lowenergy y-rays ( < 1 0 0 keV)detection the standard
plastics and liquid scintillators are loaded with lead
or tin 44'93'117) which increase strongly the detection
efficiency. The light yield of loaded plastics is
reduced because of quenching of the light by Pb
or Sn admixtures. The effective light may be larger, however, because of detection of X-rays in
the loaded plastics due to the photoeffect. The
usefulness of the loaded plastics is limited to lowenergy y-rays and unfortunately nothing is gained
for high-energy y-rays. A need for fast inorganic
scintillators arises at the moment. The NaI(TI) and
NaI scintillators give a time resolution 36,~8-12°)
several times worse than that measured with the
best plastics.
By arranging plastic and NaI(TI) detectors so
that the Compton scattered y-rays escaping from
29
the plastic are absorbed in the NaI/TI/ it is possible by external summing to obtain well-resolved
full energy peaks as demonstrated in ref. 121.
Kluge and Thomas ~22) have performed measurements in the picoseconds region by centroid shift
self-comparison using combined plastic-NaI/TI/
detectors. Because of geometry effects, the delay
of light collection in the plastic detector is energy
dependent and this effect was carefully studied.
One could imagine future systems based on
microchannel photodetectors with mosaic anodes
to compensate for light collection problems.
A very fast response of a multicrystalline
ZnO(Ga) scintillator was reported by Luckeym). A
decay time equal to 0.34 ns and a fwhm equal to
250 ps were recently measured by Tirsell et al)3).
However, because of the multicrystalline structure
of this scintillator very thin samples for o~-particle
detection must be used at present. The light yield
for 5 MeV o~-particles is larger than that of plastics, but there is no well-defined energy peak in
the spectrum27).
The authors are very much indebted to Prof. Z.
Sujkowski and Dr. H. Loft Nielsen for their
stimulating interest in the work.
References
~) L. G. Hyman, R. M. Schwartz and R. A. Schulter, Rev.
Sci. Instr. 35 (1964) 393.
2) R. E. Bell, in Beta- and gamma-ray spectroscopy (ed. K.
Siegbahn; North-Holland Publ. Co. Amsterdam, 1955).
3) A. Schwarzschild, Nucl. Instr. and Meth. 21 (1963) 1.
4) M. Benitz, Nucl. Instr. and Meth. 22 (1963) 238.
5) R. E. Bell, in Alpha-, beta- and gamma-ray spectroscopy
(ed. K. Siegbahn; North-Holland Publ. Co., Amsterdam,
1965).
6) A. Ogata and C. J. Tao, Nucl. Instr. and Meth. 69 (1969)
344.
7) V. Meiling and F. Stary, Nanosecond pulse techniques
(Akademie Verlag, Berlin, 1969).
8) A. Schwarzschild and E. K. Warburton, Ann. Rev. Nucl.
Sci. 18 (1968) 265.
9) C. W. W. Williams and D. A. Gedecke, High resolution
time spectroscopy I, Scintillation counters, ORTEC, Application Note, 1968.
J0) D. B. Fossan and E. K. Warburton, in Nuclear spectroscopy and reactions (ed. J. Cerny; Academic Press, New
York, 1974).
tl) E. Gatti and V. Svelto, Nucl. Instr. and Meth. 43 (1966)
248.
12) j. B. Birks, J. Phys. B! (1968) 946.
13) j. B. Birks and R. W. Pringle, Proc. Roy. Soc. Edinburgh
(A) 70 (1972) 233.
14) j. B. Birks, J. Phys. B3 (1970) 1704.
15) j. B. Birks and J. C. Conte, Proc. Roy. Soc. A 303 (1968)
85.
"30
M. MOSZYlqSKI AND B. BENGTSON
16) T. Forster, Zeits. f'tir Natufforsch. 4a (1949) 321.
17) L. M. Bollinger and G. E. Thomas, Rev. Sci. Instr. 32
(1961) 1044.
18) A. Raviart and V. Koechlin, Nucl. Instr. and Meth. 29
(1964) 45,
tg) L. G. Hyman, Rev. Sci. Instr. 36 (1965) 193.
20) F. J. Lynch, IEEE Trans. Nucl. Sci. NS-15, no. 3 (1968)
102.
21) F. T. Kuchnir and F. J. Lynch IEEE Trans. Nucl. Sci.
NS-15 , no. 3 (1968) 107.
22) F. J. Lynch, IEEE Trans. Nucl. Sci. NS-22, (Febr. 1975)
58.
23) B. Bengtson and M. Moszyfiski, Nucl. Instr. and Meth. 75
(1969) 152.
24) B. Bengtson and M. Moszy~ski, Nucl. Instr. and Meth. 81
(1970) 109.
25) j. Bialkowski, Z. Moroz and M. Moszyfiski, Nucl. Instr.
and Meth. 117 (1974) 221.
26) B. Bengtson and M. Moszyfiski, Nucl. Instr. and Meth.
117 (1974) 227.
27) T. Batsch, B. Bengtson and M. Moszyfiski, Nucl. Instr.
and Meth. 125 (1975) 443.
28) M. Moszyfiski and B. Bengtson, Nucl. Instr. and Meth.
142 (1977) 417.
29) B. Bengtson and M. Moszyfiski, Nucl. Instr. and Meth.
155 (1978) 221.
30) p. B. Lyons, C. R. Hurlbut and L. P. Hocker, Nucl. Instr.
and Meth. 133 (1976) 175.
3J) M. Moszyfiski, Nucl. Instr. and Meth. 153 (1978) 439.
32) p. B. Lyons, S. E. Caldwell, L. P. Hocker, D. G. Crandall,
P. A. Zagarino, .I. Cheng, G. Tirsell and C. R. Hurlbut,
IEEE Trans. Nucl. Sci. NS-24, no. 1 (1977) 177.
33) K. G. Tirsell, G. R. Tripp, E. M. Lent, R. A. Lerche, J.
C. Cheng, L. Hocker and P. B. Lyons, IEEE Trans. Nucl.
Sci. NS-24 no. 1 (1977) 250.
34) R. G. Bennet, ,i. Chem. Phys. 41 (1964) 3037.
35) M. Cocchi and A. Rota, Nucl. Instr. and Meth. 46 (1967)
136.
36) R. Nutt, PhD Thesis (Univ, of Tennessee, 1969).
37) M. Cocchi and A. Rota, Nucl. Instr. and Meth. 55 (1967)
365.
38) M. Moszy~ski, Nucl. Instr. and Meth. 134 (1976) 77.
39) T. Batsch and M. Moszyfiski, Nucl. Instr. and Meth. 123
(1975) 341.
40) B. Sipp and J. A. Miehe, Nucl. Instr. and Meth. i14 (1974)
255.
40 P. B. Lyons and J. Stevens, Nucl. Instr. and Meth. !14
(1974) 313.
42) j. Kirkbride, E. C. Yates and D. G. Crandall, Nucl. Instr.
and Meth. 52 (1967) 293.
43) T. M. Kelly, J. A. Merrigan and R. M. Lambrecht, Nucl.
Instr. and Meth. 109 (1973) 233.
44) Nuclear Enterprises, Catalog 1974.
45) R. Kunze and R. Langkau, Nucl. Instr. and Meth. 91
(1971) 667.
46) Th. Binkert, H. P. Tschanz and P. E. Zinski, J. Luminescence 5 (1972) 187.
47) A. Houdayer, S. K. Mark and R. E. Bell, Nucl. Instr. and
Meth. 59 (1968) 319.
48) M. Bertolaccini, S. Cova and C. Bussolatti, Proc. Nuclear
electronics symposium (Versailles, France, 1968).
49) j. Bialkowski and M. Moszyr~ski, Nucl. Instr. and Meth.
105 (1972) 51.
50) M. D. Hull, Fast response photomultipliers Application
book (Philips 1971).
51) M. Moszyflski and ,i. Vacher, Nucl. instr, and Meth. 141
(1977) 319.
52) G. Pietri, Proc. Conf. on InstrumentsJbr high energy physics
(ed. Stipcich, 1973) p. 566.
53) j. A. Miehe and G. Knispel, Comp. Rend. Acad. Sci. 273B
(1971) 285.
54) H. Lami, ,i. T. D'Alession, J. Zampach, R. Radicella and
J. M. Kesque, Nucl. Instr. and Meth. 92 (1971) 333.
55) C. C. Lo and B. Lescovar, IEEE Trans. Nucl. Sci. NS-21,
no. 1 (1974) 93.
56) C. R. Kerns, IEEE Trans Nucl. Sci., NS-14, no. 1 (1967)
449.
57) D. Vallat, Onde Electr. 49 (1969) 804.
58) Ph. Chevalier, J. P. Boutet and G. Pietri, IEEE Trans.
Nucl. Sci., NS-17, no. 3 (1970) 75.
59) F. de la Barre, Nucl. Instr. and Meth. 102 (1972) 77.
6o) B. Lescovar and C. C. Lo, IEEE Trans. Nucl. Sci. NS-19,
no. 3 (1972) 50.
61) B. Sipp and J. Miehe, Nucl. Instr. and Meth., 114 (1974)
249.
62) B. Lescovar and C. C. Lo, Nucl. Instr. and Meth. 123
(1975) 249.
63) G. Breuze, P. Sawine, Proc. Nztclear electronics symposiunl
(Versailles, France, 1968).
64) M. Bertolaccini, G. Bussolati, S. Cova, S. Donati and V.
Svelto, Nucl. Instr. and Meth. 51 (1967) 325.
65) R. Reisse, R. Creecy and S. K. Poultncy, Rev. Sci. Instr.
44 (1973) 1966.
66) Philips data.
67) 'i. Bialkowski, PhD. Thesis (INR Warsaw, Poland, 1972).
68) R. E. McHose, RCA Application Note, AN-4884.
69) R. Nutt, IEEE Trans. Nucl. Sci. NS-14, no. I (1967) II0.
70) p. D. Compton Jr. and W. A. Johnson, IEEE Trans. Nucl.
Sci. NS-14, no. 1 (1967) 116.
71) p. R. Orman, Nucl. Instr. and Meth. 21 (1963) 121.
72) D. L. Wieber and H. W. Lefevre, IEEE Trans. Nucl. Sci.
NS-13, no. 1, (1966) 406.
73) R. E. Bell, Nucl. Instr. and Meth. 42 (1966) 211.
74) D. A. Gedcke and W. ,i. McDonald, Nucl. Instr. and
Meth. 58 (1968) 253.
7s) D. A. Gedcke and W. ,i. McDonald, Nucl. Instr. and
Meth. 55 (1967) 377.
76) M. Post and L. ,i. Schiff, Phys. Rev. 80 (1950) 113.
77) E. Gatti and V. Svelto, Nucl. Instr. and Meth. 4 (1959)
189.
78) E. Gatti and V. Svelto, Nucl. Instr. and Meth. 30 (1964)
213.
79) S. Colombo, E. Gatti, M. Pignanelli, Nuovo Cimento 5
(1957) 1739.
80) R. Euling, J. Appl. Phys. 35 (1964) 1391.
81) S. Donati, E. Gatti and V. Svelto, Nucl. Instr. and Meth.
46 (1967.) 165.
82) M. A. EI-Wahab and J. V. Kane, Nucl. Instr. and Meth.
15 (1962) 15.
83) M. A. EI-Wahab and M. Gazzaly, Nuovo Cimento, 47B
(1967) 56,
84) M. A. EI-Wahab, M. Sakka and M. A. EI-Salam, Nucl.
Instr. and Meth. 59 (1968) 344.
85) M. A. EI-Wahab and M. A. EI-Salam, Nucl. Instr. and
Meth. 78 (1970) 325.
86) B. Sigfridsson, Nucl. Instr. and Meth. 59 (1967) 13.
TIMING WITH PLASTIC S C I N T I L L A T I O N DETECTORS
ST) G. Bertollini, V. Mandl, A. Rota and M. Cocchi, Nucl.
Instr. and Meth. 42 (1966) 109.
ss) W. M. Currie, R. E. Azume and G. M. Lewin, Nucl. Instr.
and Meth. 13 (1961) 215.
sg) W. Bartl and P. Weinzierl, Rev. Sci. Instr. 34 (1963) 252.
90) G. Present, A. Schwarzschild, 1. Spirin and N. Wotherspoon, Nucl. Instr. and Meth. 31 (1964) 71.
91) p. Huber, Z. Lewandowski, R. Plattner, C. Poppelbaum
and R. Wagner, Nucl. Instr. and Meth. 14 (1961) 13.
92) R. Richter, Ann. Phys. 6 (1961) 1437.
93) J. Jastrzebski, M. Moszyflski and A. Zglifiski, Nukleonika
II (1966) 471.
94) j. A. Miehe, E. Ostertag and A. Coche, IEEE Trans. Nucl.
Sci. NS-13, no. 3 (1966) 127.
95) W. J. McDonald and D. A. Gedcke, Nucl. Instr. and
Meth. 55 (1967) 1.
96) M. Bonitz, W. Meiling and F. Stary, Nucl. Instr. and
Meth. 29 (1964) 309.
97) W. Brunner, Nucl. Instr. and Meth. 30 (1964) 109.
9s) G. Bertollini, M. Cocchi, V. Mahdi and A. Rota, IEEE
Trans Nucl. Sci. NS 13, no. 3 (1966) 119.
99) M. Hesse, PhD Thesis (University of Lyon, France, 1965).
100) D. Porter, J. McDonald and D. T. Stewart, Nucl. Instr.
and Meth. 44 (1966) 309.
to1) S. Sanyal, S. C. Pancholi and L. Gupta, Nucl. Instr. and
Meth. 136 (1976) 157.
1o2) S. J. Tao, J. Bell and J. H. Green, Nucl. Instr. and Meth.
35 (1965) 222.
103) R. E. Bell, R. L. Graham and H. E. Petch, Can. J. Phys.
30 (1952) 35.
1o4) W. Flauger and H. Schneider, Nucl. Phys. 55 (1964) 207.
Io5) H. Weisberg, Nucl. Instr. and Meth. 32 (1965) 133.
31
IO6) R. Van Zurk, Proc. Int, Symp. on Nuclear electronics
(Warsaw, September 1971).
tOT) R. E. Pixley and H. von Fellenberg, Nucl. Instr. and
Meth. 129 (1975) 487.
1o8) P. B. Lyons and L. P. Hocker, private communication.
t09) H. O. Wirth, F. U. Herrman, G. Herrman and W, Kern,
Proc. Int. Syrup, on Organic crystals (ed. D. Horrocks;
Gordon and Breach, New York, 1968).
ItO) B. Bengtson and M. Moszyfiski, unpublished data.
Ill) W. Pfeffer, B. Kohlmeyer and F. W. Schneider, Nucl.
Instr. and Meth. 107 (1973) 121.
t2) J. Girard and M. Bolore, Nucl. Instr. and Meth. 140 (1977)
279.
13) C. E. Catchpole, IEEE Trans. Nucl. Sci. NS-19, no. I
(1972) 360.
14 G. Pietri, IEEE Trans. Nucl. Sci. NS-22, no. 5 (1975) 2084.
15 C. C. Lo, P. Lecomte and B. Lescovar, IEEE Trans. Nucl.
Sci. NS-24, no. I (1977).
116 S. Dhawan and R. Majka, IEEE Trans. Nucl. Sci. NS-24,
no. 1 (1977)270.
117 L. A. Eriksson, C. M. Tsai, Z. H. Cho and C. R. Hurlbut,
Nucl. Instr. and Meth. 122 (1974) 373.
118 F. J. Lynch, IEEE Trans. Nucl. Sci. NS-13, (1966) 140.
119 C. Hohenemser, R. Reno and A, P. Mills, IEEE Trans.
Nucl. Sci. NS-17, no. 3 (1970) 390.
~20) R. Van Zurk, F, B. Lopes and J. Ros, Nucl. Instr. and
Meth. 120 (1974) 61.
121) B. Bengtson and M. Moszyfiski, Nucl. Instr. and Meth.
134 (1970) 133.
122) A. Kluge and W. Thomas, Nucl. Instr. and Meth. 134
(1976) 525.
123) D. Luckey, Nucl. Instr. and Meth. 62 (1968) 119.